Oldest pages
From Maths
Showing below up to 500 results in range #501 to #1,000.
View (previous 500 | next 500) (20 | 50 | 100 | 250 | 500)
- Books:Elements of Algebraic Topology - James R. Munkres (07:31, 21 July 2016)
- Group action (23:28, 21 July 2016)
- Permutation (23:42, 21 July 2016)
- Permutation of a set (23:59, 21 July 2016)
- Books:Rings, Fields and Groups - An introduction to abstract algebra - R. B. J. T. Allenby (00:00, 22 July 2016)
- Klein-4 group (00:19, 22 July 2016)
- Overview of the group isomorphism theorems (00:21, 22 July 2016)
- Variance (19:45, 24 July 2016)
- Two-phase commit (18:03, 26 July 2016)
- Linear combination (07:37, 29 July 2016)
- Infimum (08:55, 29 July 2016)
- Notes:Generalising the limit (11:34, 30 July 2016)
- Axiom of completeness (13:06, 30 July 2016)
- Notes:The foundations of Mathematics - Kunen (02:38, 31 July 2016)
- The (pre-)measure of a set is no more than the sum of the (pre-)measures of the elements of a covering for that set/Statement (20:44, 31 July 2016)
- The (pre-)measure of a set is no more than the sum of the (pre-)measures of the elements of a covering for that set (21:03, 31 July 2016)
- Task:Continuity types (22:38, 4 August 2016)
- Product (00:03, 7 August 2016)
- Adjunction topology (00:12, 7 August 2016)
- Adjunction (00:13, 7 August 2016)
- Task:Characteristic property of the subspace topology (02:59, 7 August 2016)
- Task:Characteristic property of the coproduct topology (04:38, 7 August 2016)
- Books:Topology - An Introduction with Applications to Topological Groups - George McCarty (06:15, 8 August 2016)
- Topological group (06:23, 8 August 2016)
- Notes:Basis for a topology/Attempt 2 (10:14, 8 August 2016)
- Notes:Basis for a topology/New terminology (10:57, 8 August 2016)
- Notes:Topology - Munkres (10:18, 9 August 2016)
- Notes:Topology - Munkres/Section 68 (11:57, 9 August 2016)
- Notes:Dual basis (08:43, 12 August 2016)
- Notes:Advanced Linear Algebra - Roman (13:23, 13 August 2016)
- Notes:Advanced Linear Algebra - Roman/Chapter 1 (14:35, 13 August 2016)
- Notes:Homomorphism (23:44, 13 August 2016)
- Notes:Advanced Linear Algebra - Roman/Chapter 2 (11:12, 14 August 2016)
- Notes:Tangent space (19:42, 15 August 2016)
- Basis (13:40, 16 August 2016)
- Books:Advanced Linear Algebra - Steven Roman (14:09, 16 August 2016)
- R^n is a topological vector space (14:25, 16 August 2016)
- Measure (14:39, 16 August 2016)
- Notes:Basis for a topology/McCarty (16:58, 16 August 2016)
- Extending pre-measures to outer-measures (16:59, 17 August 2016)
- Epsilon form of inequalities (17:03, 17 August 2016)
- Extending pre-measures to measures (17:27, 17 August 2016)
- Pre-measure/New page (21:25, 17 August 2016)
- Ring of sets/Definition (17:21, 18 August 2016)
- Ring of sets (17:21, 18 August 2016)
- Semi-ring of sets/Definition (17:25, 18 August 2016)
- Semi-ring of sets (17:25, 18 August 2016)
- Distributivity of intersections across unions (23:19, 18 August 2016)
- The ring of sets generated by a semi-ring is the set containing the semi-ring and all finite disjoint unions (18:33, 19 August 2016)
- Types of set algebras/Type table (20:00, 19 August 2016)
- Types of set algebras/Measure theory summary table (20:05, 19 August 2016)
- Types of set algebras (20:06, 19 August 2016)
- A pre-measure on a semi-ring may be extended uniquely to a pre-measure on a ring (22:16, 19 August 2016)
- Set (22:28, 19 August 2016)
- Semi-ring of half-closed-half-open intervals (00:23, 20 August 2016)
- Doctrine:Measure theory terminology/Proposals (21:29, 20 August 2016)
- Outer splicing set (22:09, 20 August 2016)
- Properties of classes of sets closed under set-subtraction (11:38, 21 August 2016)
- Site projects:Patrolling measure theory/Task list (11:40, 21 August 2016)
- Hereditary (16:37, 22 August 2016)
- Hereditary set (16:46, 22 August 2016)
- Partial-function (22:26, 23 August 2016)
- Hereditary system generated by (23:36, 23 August 2016)
- Notes:First order language (09:22, 28 August 2016)
- Task:Rings and sigma-rings (15:52, 30 August 2016)
- A subset of a topological space is open if and only if it is a neighbourhood to all of its points (00:27, 6 September 2016)
- Term (FOL) (05:15, 8 September 2016)
- Books:Mathematical Logic - Foundations for Information Science - Wei Li (05:17, 8 September 2016)
- Formula (FOL) (05:37, 8 September 2016)
- Herbrand domain (08:35, 8 September 2016)
- Hintikka set (08:50, 8 September 2016)
- Editing guide/Templates (10:01, 8 September 2016)
- Editing guide/Templates/Page categorisation (10:11, 8 September 2016)
- Principle of excluded middle (10:29, 8 September 2016)
- First order language (10:45, 8 September 2016)
- Structure (FOL) (10:55, 8 September 2016)
- Domain (FOL) (06:42, 10 September 2016)
- Interpretation (FOL) (06:54, 10 September 2016)
- Assignment (FOL) (07:14, 10 September 2016)
- Substitution assignment (FOL) (07:18, 10 September 2016)
- Model (FOL) (07:31, 10 September 2016)
- Semantics of terms (FOL) (07:49, 10 September 2016)
- Truth values (FOL) (08:09, 10 September 2016)
- Semantics of logical connectives (FOL) (07:46, 11 September 2016)
- Semantics of formulas (FOL) (07:53, 11 September 2016)
- Satisfiable formula (11:00, 11 September 2016)
- Valid formula (11:10, 11 September 2016)
- Logical consequence (FOL) (11:22, 11 September 2016)
- If A is a logical consequence of Gamma then the formula set of Gamma union the negation of A is not satisfiable (11:25, 11 September 2016)
- Equivalent formulas (11:32, 11 September 2016)
- Notes:Quotient topology/Table (16:09, 13 September 2016)
- Demonstrating why category arrows are best thought of as arrows and not functions (12:29, 15 September 2016)
- Pre-measure on a semi-ring (12:40, 15 September 2016)
- HomotopyPage (12:53, 15 September 2016)
- Homotopic maps (13:26, 15 September 2016)
- Notes:Homotopy terminology/Terminology (14:40, 16 September 2016)
- Homotopy is an equivalence relation on the set of all continuous maps between spaces/proof (07:33, 18 September 2016)
- Unix philosophy/Eric S. Raymond (02:12, 20 September 2016)
- Unix philosophy (02:12, 20 September 2016)
- The basis criterion (topology)/Statement (00:08, 23 September 2016)
- The basis criterion (topology) (00:11, 23 September 2016)
- Notes:Ascii table (07:32, 23 September 2016)
- Product topology (20:32, 23 September 2016)
- Characteristic property of the product topology/Statement/Diagram (20:53, 23 September 2016)
- Characteristic property of the product topology/Statement (20:55, 23 September 2016)
- Characteristic property of the product topology (21:06, 23 September 2016)
- Editing guide (18:48, 24 September 2016)
- Notes:Parsing (19:06, 24 September 2016)
- Characteristic property of the disjoint union topology/Statement (20:05, 25 September 2016)
- Characteristic property of the disjoint union topology (20:07, 25 September 2016)
- Disjoint union (set) (20:21, 25 September 2016)
- Characteristic property of the disjoint union topology/Proof (20:31, 25 September 2016)
- Characteristic property of the subspace topology/Statement (22:45, 25 September 2016)
- Topological embedding (22:53, 25 September 2016)
- Subspace topology (23:04, 25 September 2016)
- The composition of continuous maps is continuous (23:14, 25 September 2016)
- Canonical injection of the subspace topology (23:22, 25 September 2016)
- Characteristic property of the subspace topology (23:25, 25 September 2016)
- Disjoint union (23:29, 25 September 2016)
- Disjoint union topology (23:47, 25 September 2016)
- Canonical injections of the disjoint union topology (00:16, 26 September 2016)
- Box topology (10:19, 26 September 2016)
- Canonical projections of the product topology (11:00, 26 September 2016)
- Bijection (11:49, 26 September 2016)
- Every injection yields a bijection onto its image (11:53, 26 September 2016)
- Every bijection yields an inverse function (12:24, 26 September 2016)
- The canonical injections of the disjoint union topology are topological embeddings (12:34, 26 September 2016)
- Closed map (19:59, 26 September 2016)
- Task:Equivalent properties to homeomorphism (20:25, 26 September 2016)
- Closure of a set in a topological space (10:16, 28 September 2016)
- Notes:Connected space (21:33, 30 September 2016)
- Site projects:Patrolling topology/Task list (21:36, 30 September 2016)
- Disconnected (topology)/Definition (22:15, 30 September 2016)
- A topological space is connected if and only if the only sets that are both open and closed in the space are the entire space itself and the emptyset (22:52, 30 September 2016)
- Every continuous map from a non-empty connected space to a discrete space is constant (23:02, 30 September 2016)
- A topological space is disconnected if and only if there exists a non-constant continuous function from the space to the discrete space on two elements (23:12, 30 September 2016)
- A topological space is disconnected if and only if it is homeomorphic to a disjoint union of two or more non-empty topological spaces (23:15, 30 September 2016)
- Disconnected (topology) (23:59, 30 September 2016)
- Connected (topology) (01:52, 1 October 2016)
- Disjoint (03:19, 1 October 2016)
- Non-empty (04:56, 1 October 2016)
- Connected (topology)/Equivalent conditions (00:21, 2 October 2016)
- A subset of a topological space is disconnected if and only if it can be covered by two non-empty-in-the-subset and disjoint-in-the-subset sets that are open in the space itself/Statement (09:39, 2 October 2016)
- A subset of a topological space is disconnected if and only if it can be covered by two non-empty-in-the-subset and disjoint-in-the-subset sets that are open in the space itself (09:39, 2 October 2016)
- The image of a connected set is connected (04:10, 3 October 2016)
- Exercises:Mond - Topology - 1/Pictures (11:38, 8 October 2016)
- Homeomorphic (11:52, 8 October 2016)
- Exercises:Mond - Topology - 1/Pictures/Q7 - 1 (12:31, 8 October 2016)
- Every surjective map gives rise to an equivalence relation (13:54, 8 October 2016)
- Passing to the quotient (topology) (17:43, 8 October 2016)
- Passing to the quotient (function)/Diagram (20:38, 8 October 2016)
- Canonical projection of an equivalence relation (22:33, 8 October 2016)
- Equivalence relation induced by a function (22:40, 8 October 2016)
- Factoring a function through the projection of an equivalence relation induced by that function yields an injection/Diagram (22:54, 8 October 2016)
- If a surjective function is factored through the canonical projection of the equivalence relation induced by that function then the yielded function is a bijection (12:57, 9 October 2016)
- Factoring a function through the projection of an equivalence relation induced by that function yields an injection (20:24, 9 October 2016)
- Characteristic property of the quotient topology (22:16, 9 October 2016)
- Characteristic property of the quotient topology/Statement (22:16, 9 October 2016)
- Factoring a continuous map through the projection of an equivalence relation induced by that map yields an injective continuous map (22:23, 9 October 2016)
- If a surjective continuous map is factored through the canonical projection of the equivalence relation induced by that map then the yielded map is a continuous bijection (22:32, 9 October 2016)
- A subspace of a Hausdorff space is Hausdorff (12:51, 10 October 2016)
- Exercises:Mond - Topology - 1 (18:29, 10 October 2016)
- Notes:Modules (17:18, 11 October 2016)
- Passing to the quotient (topology)/Statement (20:23, 11 October 2016)
- Passing to the quotient (function) (20:49, 11 October 2016)
- Exercises:Mond - Topology - 1/Pictures/Q6P1 - 1 (22:35, 11 October 2016)
- Exercises:Mond - Topology - 1/Question 7 (23:26, 11 October 2016)
- Exercises:Mond - Topology - 1/Question 8 (00:13, 12 October 2016)
- Exercises:Mond - Topology - 1/Question 6 (12:26, 12 October 2016)
- Exercises:Mond - Topology - 1/Question 9 (12:34, 12 October 2016)
- Properties of the pre-image of a function (00:51, 14 October 2016)
- A map is continuous if and only if the pre-image of every closed set is closed (01:39, 14 October 2016)
- Continuous map (01:44, 14 October 2016)
- Continuous map/Refactoring tasks (01:46, 14 October 2016)
- Open neighbourhood (01:51, 14 October 2016)
- A map is continuous if and only if each point in the domain has an open neighbourhood for which the restriction of the map is continuous on (06:01, 14 October 2016)
- A set is open if and only if every point in the set has an open neighbourhood contained within the set (06:06, 14 October 2016)
- Pasting lemma (07:07, 14 October 2016)
- Homotopy is an equivalence relation on the set of all continuous maps between spaces (23:37, 14 October 2016)
- Path (23:47, 14 October 2016)
- Path (topology) (23:58, 14 October 2016)
- Definitions and iff (00:14, 15 October 2016)
- Concatenation of paths and loops (homotopy) (00:57, 15 October 2016)
- Notes:Homology (07:30, 15 October 2016)
- Notes:Homology/Real projective plane (01:48, 16 October 2016)
- Notes:Homology/Torus (01:50, 16 October 2016)
- U-ring/Motivation (04:11, 16 October 2016)
- Q-ring (04:28, 16 October 2016)
- C-ring (04:30, 16 October 2016)
- ASN (04:31, 16 October 2016)
- Ring homomorphism (04:50, 16 October 2016)
- Ring (05:02, 16 October 2016)
- Group (07:17, 16 October 2016)
- Fibre (12:59, 16 October 2016)
- Saturated (13:02, 16 October 2016)
- Saturated set with respect to a function (13:08, 16 October 2016)
- Equivalent conditions to a set being saturated with respect to a function (13:15, 16 October 2016)
- Quotient topology (13:34, 16 October 2016)
- Equivalent conditions to a map being a quotient map (13:38, 16 October 2016)
- Exercises:Mond - Topology - 2/Section B/Question 6/Picture (02:48, 18 October 2016)
- Exercises:Mond - Topology - 2/Section B/Question 5 (08:30, 18 October 2016)
- Exercises:Mond - Topology - 2/Section B (11:24, 19 October 2016)
- Exercises:Mond - Topology - 2/Section B/Question 8 (11:57, 19 October 2016)
- Exercises:Mond - Topology - 2 (12:23, 19 October 2016)
- Exercises:Mond - Topology - 2/Section B/Question 6 (12:27, 19 October 2016)
- Exercises:Mond - Topology - 2/Section B/Question 7 (12:30, 19 October 2016)
- Exercises:Rings and Modules - 2016 - 1 (13:48, 19 October 2016)
- Exercises:Rings and Modules - 2016 - 1/Problem 3 (13:52, 19 October 2016)
- Exercises:Rings and Modules - 2016 - 1/Problem 4 (13:53, 19 October 2016)
- Exercises:Measure Theory - 2016 - 1/Section A (14:01, 19 October 2016)
- Exercises:Measure Theory - 2016 - 1/Section B (14:03, 19 October 2016)
- Exercises:Measure Theory - 2016 - 1 (14:04, 19 October 2016)
- Exercises:Rings and Modules - 2016 - 1/Problem 1 (16:05, 19 October 2016)
- If and only if (16:21, 19 October 2016)
- Ring/New page (16:29, 19 October 2016)
- U-ring (16:32, 19 October 2016)
- Exercises:Rings and Modules - 2016 - 1/Problem 2 (16:57, 19 October 2016)
- Characteristic property of the direct product module/Statement/Diagram (21:01, 19 October 2016)
- Characteristic property of the direct product module/Statement (21:02, 19 October 2016)
- Characteristic property of the direct product module (21:17, 19 October 2016)
- Homomorphism (22:04, 19 October 2016)
- Direct product module (22:19, 19 October 2016)
- Module homomorphism (22:20, 19 October 2016)
- Module (22:40, 19 October 2016)
- Coproduct (13:22, 20 October 2016)
- Direct sum module (13:25, 20 October 2016)
- Characteristic property of the direct sum module/Statement/Picture (13:52, 20 October 2016)
- Characteristic property of the direct sum module/Statement (14:02, 20 October 2016)
- Characteristic property of the direct sum module (14:04, 20 October 2016)
- External direct sum module (14:05, 20 October 2016)
- Notes:Chain complex of modules (17:15, 20 October 2016)
- Notes:Infinity notation (15:23, 21 October 2016)
- Exercises:Measure Theory - 2016 - 1/Section B/Problem 1 (14:09, 23 October 2016)
- Xypic (17:14, 23 October 2016)
- Module factorisation theorem (19:51, 23 October 2016)
- Quotient module (20:00, 23 October 2016)
- Quotient group (20:15, 23 October 2016)
- Notes:Coset stuff (21:17, 25 October 2016)
- Notes:Coset stuff/Quotient group (15:57, 26 October 2016)
- Notes:Rings and u-rings (16:33, 26 October 2016)
- Books:Warwick 2014 Lecture Notes - Functional Analysis - Richard Sharp (18:56, 28 October 2016)
- Subset of (19:21, 28 October 2016)
- The intersection of two sets is non-empty if and only if there exists a point in one set that is in the other set (19:31, 28 October 2016)
- Commutativity of intersection (19:32, 28 October 2016)
- Equivalent statements to a set being dense (20:18, 28 October 2016)
- Neighbourhood (20:23, 28 October 2016)
- A set is dense if and only if every non-empty open subset contains a point of it (20:29, 28 October 2016)
- Task:Unnamed inequality (01:38, 29 October 2016)
- Functional Analysis (subject) (23:08, 29 October 2016)
- Bounded set (23:31, 29 October 2016)
- Equivalent conditions to a set being bounded/Statement (23:41, 29 October 2016)
- Equivalent conditions to a set being bounded/1 implies 2 (23:45, 29 October 2016)
- Equivalent conditions to a set being bounded/2 implies 1 (23:45, 29 October 2016)
- Notes:Homotopy terminology (09:00, 31 October 2016)
- Doctrine:Homotopy terminology (09:01, 31 October 2016)
- Exercises:Mond - Topology - 4 (14:29, 31 October 2016)
- Exercises:Mond - Topology - 4/Section B (14:32, 31 October 2016)
- Exercises:Mond - Topology - 4/Section B/Question 6 (15:49, 31 October 2016)
- Notes:Algebraic Topology - Hatcher (22:02, 31 October 2016)
- Loop (20:32, 1 November 2016)
- Loop (topology) (20:32, 1 November 2016)
- Notes:Algebraic Topology - Hatcher/Chapter 0 (20:57, 1 November 2016)
- Constant loop based at a point (21:03, 1 November 2016)
- Constant function (21:12, 1 November 2016)
- Omega(X,b) (04:47, 3 November 2016)
- The set of continuous functions between topological spaces (05:02, 3 November 2016)
- Index of spaces, sets and classes (05:06, 3 November 2016)
- C(I,X) (05:08, 3 November 2016)
- The fundamental group (16:10, 4 November 2016)
- Proof that the fundamental group is actually a group/Outline (18:31, 4 November 2016)
- Proof that the fundamental group is actually a group/Outline/Picture (01:52, 6 November 2016)
- Homotopy concatenation (05:09, 6 November 2016)
- Loop concatenation (09:17, 6 November 2016)
- Path concatenation (topology) (09:19, 6 November 2016)
- Homotopy invariance of loop concatenation (09:21, 6 November 2016)
- IT-Ebooks.info & obtaining pdfs of books (11:10, 7 November 2016)
- Proof that the fundamental group is actually a group (11:20, 8 November 2016)
- Proof that the fundamental group is actually a group/Proof (11:44, 8 November 2016)
- Notes:Fundamentals of Algebraic Topology - Weintraub (21:53, 8 November 2016)
- Invariant of an equivalence relation (18:58, 9 November 2016)
- Homotopy invariance of path concatenation (19:11, 9 November 2016)
- Every lingering sequence has a convergent subsequence/Statement (19:57, 9 November 2016)
- Exists a unique (20:08, 9 November 2016)
- Books:Calculus on Manifolds - Spivak (09:49, 11 November 2016)
- Books:Analysis on Manifolds - James R. Munkres (09:49, 11 November 2016)
- Notes:Differential notation and terminology (09:56, 11 November 2016)
- Doctrine:Differentiation notation & terminology (10:34, 11 November 2016)
- Strong derivative/Infobox (14:06, 13 November 2016)
- Quotient by an equivalence relation (14:16, 13 November 2016)
- Equivalence classes are either equal or disjoint (14:36, 13 November 2016)
- Total derivative (01:27, 15 November 2016)
- Initial and final compared (category theory) (20:25, 15 November 2016)
- Initial (category theory) (20:30, 15 November 2016)
- Final (category theory) (20:32, 15 November 2016)
- Subsequence/Definition (21:54, 16 November 2016)
- Subsequence (23:27, 16 November 2016)
- Negation of implies (21:05, 17 November 2016)
- The vector space of all linear maps between two spaces (21:16, 17 November 2016)
- Books:Functional Analysis - George Bachman and Lawrence Narici (21:25, 17 November 2016)
- A linear map is injective if and only if the image of every non-zero vector is a non-zero vector (21:29, 17 November 2016)
- Series (summation)/Infobox (20:05, 18 November 2016)
- Series (summation) (20:13, 18 November 2016)
- Notes:Polynomial ring (19:42, 19 November 2016)
- Polynomial u-ring (02:34, 20 November 2016)
- Absolute value (object) (05:25, 21 November 2016)
- UTLOC:1 (10:03, 22 November 2016)
- If a real series converges then its terms tend to zero (10:09, 22 November 2016)
- Real sequence (05:44, 23 November 2016)
- Operations on convergent sequences of real numbers (05:45, 23 November 2016)
- Comparison test for real series/Statement (06:16, 23 November 2016)
- A monotonically increasing sequence bounded above converges (07:21, 23 November 2016)
- Comparison test for real series (07:28, 23 November 2016)
- Bernstein polynomial/Definition (10:44, 25 November 2016)
- Bernstein polynomial (10:44, 25 November 2016)
- Notes:Richard Sharp question (21:03, 25 November 2016)
- Example:A smooth function that is not real analytic (04:25, 27 November 2016)
- Transposition (group theory) (10:28, 30 November 2016)
- Example:Permutation (group theory) of S5/Body (12:11, 30 November 2016)
- Example:Permutation (group theory) of S5 (12:13, 30 November 2016)
- Symmetric group (12:21, 30 November 2016)
- Notes:An introduction to manifolds - Loring W. Tu (14:07, 1 December 2016)
- Quotient (22:20, 1 December 2016)
- Quotient vector space/New page (23:09, 1 December 2016)
- Quotient vector space (23:09, 1 December 2016)
- Group factorisation theorem (22:55, 3 December 2016)
- Characteristic property of the tensor product (23:51, 3 December 2016)
- Task:Factoring vector spaces (00:23, 4 December 2016)
- Basis for the tensor product (23:56, 6 December 2016)
- Basis for the tensor product/Statement (23:56, 6 December 2016)
- Books:Linear Algebra via Exterior Products - Sergei Winitzki (05:35, 7 December 2016)
- Example:Canonical linear isomorphism between a one dimensional vector space and its field (05:44, 7 December 2016)
- Canonical linear map (05:54, 7 December 2016)
- The dual space to the dual space of a vector space is canonically isomorphic to the vector space (05:34, 8 December 2016)
- Notes:Dual to dual vector space (05:34, 8 December 2016)
- Dual vector space (05:35, 8 December 2016)
- A linear map is injective if and only if the kernel contains only the zero vector (05:38, 8 December 2016)
- Free group generated by (19:51, 10 December 2016)
- Free product of groups (20:35, 10 December 2016)
- Notes:Free group (20:36, 10 December 2016)
- Pointed topological space (21:26, 12 December 2016)
- Nth homotopy group (22:17, 12 December 2016)
- The composition of end-point-preserving-homotopic paths with a continuous map yields end-point-preserving-homotopic paths (22:38, 12 December 2016)
- Topological retraction/Definition (08:04, 13 December 2016)
- Deformation retraction/Definition (08:19, 13 December 2016)
- Types of topological retractions (04:26, 14 December 2016)
- Fundamental group homomorphism induced by a continuous map (04:28, 14 December 2016)
- The induced fundamental group homomorphism of a composition of continuous maps is the same as the composition of their induced homomorphisms (04:59, 14 December 2016)
- The induced fundamental group homomorphism of a composition of continuous maps is the same as the composition of their induced homomorphisms/Statement (05:01, 14 December 2016)
- The induced fundamental group homomorphism of the identity map is the identity map of the fundamental group (05:40, 14 December 2016)
- The induced fundamental group homomorphism of the identity map is the identity map of the fundamental group/Statement (05:46, 14 December 2016)
- Homeomorphic topological spaces have isomorphic fundamental groups (05:51, 14 December 2016)
- Homeomorphic topological spaces have isomorphic fundamental groups/Statement (05:56, 14 December 2016)
- A continuous map induces a homomorphism on fundamental groups (07:35, 14 December 2016)
- If the composition of two functions is a bijection then the initial map is injective and the latter map is surjective (08:27, 14 December 2016)
- Topological retraction (10:49, 14 December 2016)
- The intersection of an arbitrary family of Dynkin systems is itself a Dynkin system (15:12, 16 December 2016)
- Dynkin system generated by (15:16, 16 December 2016)
- Every set in the Dynkin system generated by is also in the sigma-algebra generated by (12:43, 17 December 2016)
- A collection of subsets is a sigma-algebra iff it is a Dynkin system and closed under finite intersections (13:21, 17 December 2016)
- A function is continuous if and only if the pre-image of every basis element is open (18:35, 17 December 2016)
- Basis for a topology (18:35, 17 December 2016)
- The image of a compact set is compact (17:20, 18 December 2016)
- Lebesgue measure (00:28, 20 December 2016)
- Index of notation/L (21:46, 20 December 2016)
- Characteristic property of the tensor product/Statement (22:07, 20 December 2016)
- Notes:Concrete tensor product (21:04, 21 December 2016)
- Tensor product of vector spaces (21:33, 22 December 2016)
- Tensor product of tensors (21:58, 22 December 2016)
- Free vector space generated by (15:00, 24 December 2016)
- Formal linear combination (15:35, 24 December 2016)
- Formal linear combination/Definition (15:36, 24 December 2016)
- Weierstrass approximation theorem (08:17, 28 December 2016)
- Finite complement topology (09:21, 30 December 2016)
- Topology (09:28, 30 December 2016)
- Interior point (topology) (09:48, 30 December 2016)
- Logical and (04:06, 1 January 2017)
- Dense (04:15, 1 January 2017)
- Algebra (linear algebra) (05:26, 1 January 2017)
- Algebra (disambiguation) (05:27, 1 January 2017)
- Index of notation for sets of continuous maps (06:06, 1 January 2017)
- Index of notation/C (06:13, 1 January 2017)
- Index of notation (06:13, 1 January 2017)
- Index of notation for sets of continuous maps/Index (06:20, 1 January 2017)
- Doctrine:Notation for sets of continuous maps (06:40, 1 January 2017)
- Order terminology (18:45, 8 January 2017)
- Exercises:Saul - Algebraic Topology - 1 (14:13, 13 January 2017)
- Exercises:Saul - Algebraic Topology - 1/Exercise 1.5 (19:34, 14 January 2017)
- N-cell (19:57, 14 January 2017)
- A compact and convex subset of Euclidean n-space with non-empty interior is a closed n-cell and its interior is an open n-cell/Statement (20:14, 14 January 2017)
- A compact and convex subset of Euclidean n-space with non-empty interior is a closed n-cell and its interior is an open n-cell (20:17, 14 January 2017)
- Topology generated by a basis (21:14, 15 January 2017)
- Topology generated by a basis/Statement (21:59, 15 January 2017)
- The relationship between logical implication and the subset relation (17:36, 16 January 2017)
- An open ball contains another open ball centred at each of its points (17:45, 16 January 2017)
- If the intersection of two open balls is non-empty then for every point in the intersection there is an open ball containing it in the intersection (20:16, 16 January 2017)
- Given two open balls sharing the same centre but with differing radius then the one defined to have a strictly smaller radius is contained in the other (20:27, 16 January 2017)
- The set of all open balls of a metric space are able to generate a topology and are a basis for that topology (22:16, 16 January 2017)
- Empty set (11:34, 17 January 2017)
- Topology induced by a metric (12:05, 17 January 2017)
- Exercises:Saul - Algebraic Topology - 1/Exercise 1.2/Lemmas (18:46, 17 January 2017)
- Exercises:Saul - Algebraic Topology - 1/Exercise 1.2 (12:03, 18 January 2017)
- Closed interval (14:19, 19 January 2017)
- Dipa/Help (13:40, 20 January 2017)
- CW-complex (14:14, 20 January 2017)
- Torus (16:11, 20 January 2017)
- Notes:CW-Complex (01:00, 23 January 2017)
- Exercises:Saul - Algebraic Topology - 2 (15:08, 23 January 2017)
- Boundary (topology) (22:57, 23 January 2017)
- Exercises:Saul - Algebraic Topology - 2/Exercise 2.5 (12:22, 25 January 2017)
- Basis (linear algebra) (13:17, 26 January 2017)
- Span (linear algebra) (13:51, 26 January 2017)
- The ell p spaces (14:30, 26 January 2017)
- Notes:Stone-Weierstrass theorem (13:29, 27 January 2017)
- Exercises:Saul - Algebraic Topology - 3 (23:29, 27 January 2017)
- Notes:Potentially invalid vertex scheme (03:36, 31 January 2017)
- Simplex (14:03, 31 January 2017)
- Index of elementary set theory equalities (14:46, 31 January 2017)
- A cap (B-C) = (A cap B) - C (15:07, 31 January 2017)
- A-(A-B) = A cap B (15:08, 31 January 2017)
- Simplicial complex (15:12, 31 January 2017)
- Geometrically independent set (15:20, 31 January 2017)
- Pre-image (22:28, 31 January 2017)
- Exercises:Saul - Algebraic Topology - 3/Exercise 3.2 (06:33, 1 February 2017)
- Books:A Guide To Advanced Real Analysis - Gerald B. Folland (13:01, 2 February 2017)
- Measurable space (13:05, 2 February 2017)
- Pre-measurable space (13:07, 2 February 2017)
- Books:Introduction To Set Theory - Third Edition, Revised and Expanded - Karel Hrbacek & Thomas Jech (12:54, 3 February 2017)
- Successor of a set (15:14, 3 February 2017)
- Inductive set (15:56, 3 February 2017)
- Books:Notes On Set Theory - Second Edition - Yiannis Moschovakis (00:05, 4 February 2017)
- Notes:Delta complex (14:28, 5 February 2017)
- A linear map is injective if and only if its kernel is trivial (15:05, 5 February 2017)
- Notes:Delta complex/Formal attempt (14:36, 6 February 2017)
- Convex set (11:27, 9 February 2017)
- Notes:Functional Analysis II (12:00, 9 February 2017)
- Convex (14:50, 9 February 2017)
- Convex function (10:54, 10 February 2017)
- Epigraph (11:04, 10 February 2017)
- Convex hull (15:54, 12 February 2017)
- The singular homology groups of a 1-point space are all trivial except the zeroth which is isomorphic to the integers (18:10, 12 February 2017)
- Exercises:Saul - Algebraic Topology - 5 (15:22, 14 February 2017)
- Exercises:Saul - Algebraic Topology - 5/Exercise 5.6 (20:13, 14 February 2017)
- Trivial (13:29, 16 February 2017)
- Trivial group (13:41, 16 February 2017)
- Topological vector space (14:03, 16 February 2017)
- A proper vector subspace of a topological vector space has no interior (17:49, 16 February 2017)
- For a vector subspace of a topological vector space if there exists a non-empty open set contained in the subspace then the spaces are equal (17:51, 16 February 2017)
- Doctrine:K (field) (18:30, 16 February 2017)
- Doctrine:K (topological space) (18:36, 16 February 2017)
- Doctrine:K (18:42, 16 February 2017)
- List of topological properties (19:33, 16 February 2017)
- Interior (topology) (20:10, 16 February 2017)
- The interior of a set in a topological space is equal to the union of all interior points of that set (20:15, 16 February 2017)
- Intermediate value theorem (17:35, 17 February 2017)
- The real line (17:50, 17 February 2017)
- Singleton (17:53, 17 February 2017)
- Real projective space (09:08, 18 February 2017)
- Vertex set of an abstract simplicial complex/Definition (11:37, 19 February 2017)
- Vertex set of an abstract simplicial complex (11:38, 19 February 2017)
- Vertex scheme of an abstract simplicial complex/Definition (11:51, 19 February 2017)
- Vertex scheme of an abstract simplicial complex (11:52, 19 February 2017)
- Abstract simplicial complex (11:54, 19 February 2017)
- Books:Combinatorial Algebraic Topology - Dmitry Kozlov (11:56, 19 February 2017)
- Locally Euclidean topological space (14:32, 20 February 2017)
- Locally Euclidean topological space of dimension n (12:40, 21 February 2017)
- Ell^p(C) is complete for p between one and positive infinity inclusive (18:12, 22 February 2017)
- Notes:Ell^p(C) is complete for p between one and positive infinity inclusive (18:56, 22 February 2017)
- Local homeomorphism (21:45, 22 February 2017)
- Hausdorff space (22:52, 22 February 2017)
- Open map (22:53, 22 February 2017)
- Homeomorphism (22:58, 22 February 2017)
- Example:A bijective and continuous map that is not a homeomorphism (23:04, 22 February 2017)
- Path-connected topological space (12:52, 23 February 2017)
- Example:Continuous maps contracting something to a point (14:35, 23 February 2017)
- Locally path-connected topological space (15:10, 23 February 2017)
- Evenly covered by a continuous map (21:54, 24 February 2017)
- Notes:Covering spaces (19:20, 25 February 2017)
- Covering map (topology)/Definition (01:22, 26 February 2017)
- Covering map (topology) (01:24, 26 February 2017)
- Topological covering space (01:35, 26 February 2017)
- Lifting of a continuous map through a covering map (01:59, 26 February 2017)
- The real numbers (21:31, 26 February 2017)
- The real numbers/Infobox (21:31, 26 February 2017)
- Borel sigma-algebra of the real line (15:48, 27 February 2017)
- Doctrine:Measure theory terminology (17:49, 27 February 2017)
- Exercises:Saul - Algebraic Topology - 7 (16:33, 28 February 2017)
- Exercises:Saul - Algebraic Topology - 7/Exercise 7.6/X Complex (16:58, 28 February 2017)
- Exercises:Saul - Algebraic Topology - 7/Exercise 7.6 (12:43, 1 March 2017)
- Unique lifting property (16:23, 2 March 2017)
- NeedEditingSpace (16:24, 2 March 2017)
- Simple function under-approximation to a numerical function (15:28, 3 March 2017)
- Notes:Simple function approximation to a numerical function (15:30, 3 March 2017)
- Exercises:Saul - Algebraic Topology - 8 (13:14, 7 March 2017)
- Given a homeomorphism all subspaces of the domain are homeomorphic to their image under the homeomorphism itself/Statement (13:24, 7 March 2017)
- Given a homeomorphism all subspaces of the domain are homeomorphic to their image under the homeomorphism itself (13:25, 7 March 2017)
- Exercises:Saul - Algebraic Topology - 8/Exercise 8.5 (15:25, 7 March 2017)
- Rewriting for-all and exists within set theory (17:26, 8 March 2017)
- Singleton (set theory) (17:38, 8 March 2017)
- Axiom of foundation (23:23, 8 March 2017)
- Singleton (set theory)/Definition (23:34, 8 March 2017)