# All pages

From Maths

All pages | Next page (Distributivity of intersections across unions) |

- 0^0
- 2-Dimensional rotation matrix
- A-(A-B) = A cap B
- ASN
- A cap (B-C) = (A cap B) - C
- A collection of subsets is a sigma-algebra if and only if it is both a p-system and a d-system
- A collection of subsets is a sigma-algebra iff it is a Dynkin system and closed under finite intersections
- 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
- 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
- A continuous map induces a homomorphism between fundamental groups
- A continuous map induces a homomorphism on fundamental groups
- A function is a measure iff it measures the empty set as 0, disjoint sets add, and it is continuous from below (with equiv. conditions)
- A function is continuous if and only if the pre-image of every basis element is open
- A linear map is injective if and only if its kernel is trivial
- A linear map is injective if and only if the image of every non-zero vector is a non-zero vector
- A linear map is injective if and only if the kernel contains only the zero vector
- A map from two sigma-algebras, A and B, is measurable if and only if for some generator of B (call it G) we have the inverse image of S is in A for every S in G
- 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
- A map is continuous if and only if the pre-image of every closed set is closed
- A monotonically increasing sequence bounded above converges
- A pair of identical elements is a singleton
- A pre-measure on a semi-ring may be extended uniquely to a pre-measure on a ring
- A proper vector subspace of a topological vector space has no interior
- A sequence consisting of the nth terms of the sequences in a Cauchy sequence of elements in any little-L space is itself a Cauchy sequence of complex numbers
- A set is bounded if and only if for all points in the space there is a positive real such that the distance from that point to any point in the set is less than the positive real
- A set is dense if and only if every non-empty open subset contains a point of it
- A set is open if and only if every point in the set has an open neighbourhood contained within the set
- 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
- 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
- A subset of a topological space is open if and only if it is a neighbourhood to all of its points
- A subspace of a Hausdorff space is Hausdorff
- A subspace of a Hausdorff space is a Hausdorff space
- 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
- A topological space is disconnected if and only if it is homeomorphic to a disjoint union of two or more non-empty topological spaces
- 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
- Abelian group
- Abs (function)
- Absolute value
- Absolute value (function)
- Absolute value (object)
- Abstract Algebra
- Abstract Algebra (subject)
- Abstract simplicial complex
- Addition of Poisson distributions
- Addition of vector spaces
- Additive function
- Additive set function
- Adjunction
- Adjunction (topology)
- Adjunction topology
- Alec's base 5 conventions
- Alec's c.d.f-sidestepping sampling method
- Alec's expected value trick
- Alec's ordered data test
- Alec's puzzles
- Alec's puzzles/Statistics
- Alec's remaining probability bound
- Alec's sample mean bound
- Alec's taxonomy of measures
- Alec's taxonomy of units
- Algebra
- Algebra (disambiguation)
- Algebra (linear algebra)
- Algebra (measure theory)
- Algebra of sets
- Algebra of sets/Infobox
- Algebras of sets
- Almost always
- Alphabet (formal languages)
- Also known as
- An injective group homomorphism means the group is isomorphic to its image
- An open ball contains another open ball centred at each of its points
- An open set is a neighbourhood to all of its points
- And (logic)
- Arc length
- Arity
- Arrow
- Arrow (category theory)
- Assignment (FOL)
- Associative
- Atlas
- Atomic formula (FOL)
- Axiom of completeness
- Axiom of completeness/Statement
- Axiom of foundation
- Axiom of regularity
- Axiom schema of replacement
- BORV
- Basis
- Basis (linear algebra)
- Basis (topology)
- Basis and coordinates
- Basis criterion (topology)
- Basis for a topology
- Basis for the tensor product
- Basis for the tensor product/Statement
- Bastard's object
- Bernstein polynomial
- Bernstein polynomial/Definition
- Bijection
- Bijective
- Bilinear form
- Bilinear map
- Bilinear map/Definition
- Bimorphism
- Binary multiplexor
- Binary relation
- Binomial distribution
- Borel sigma-algebra
- Borel sigma-algebra generated by
- Borel sigma-algebra generated by/Claim 1
- Borel sigma-algebra of the real line
- Borv
- Boundary (topology)
- Bounded
- Bounded (linear map)
- Bounded (sequence)
- Bounded (set)
- Bounded linear map
- Bounded sequence
- Bounded set
- Box topology
- C(I,X)
- C(X,Y)
- C( )0,1( ,R) is not complete when considered with the L^1 norm
- C-ring
- CW-complex
- Canonical injection of the subspace topology
- Canonical injections of the disjoint union topology
- Canonical linear map
- Canonical projection of an equivalence relation
- Canonical projection of the equivalence relation
- Canonical projection of the product topology
- Canonical projections of the product topology
- Cantor's construction of the real numbers
- Cantor's construction of the real numbers/Definition
- Cardinality
- Cartesian product
- Categorical coproduct
- Categorical coproducts
- Categorical isomorphism
- Categorical product
- Categorical products
- Category
- Category Theory (subject)
- Cauchy-Schwarz inequality
- Cauchy-Schwarz inequality for inner product spaces
- Cauchy criterion for convergence
- Cauchy sequence
- Cauchy sequence/Definition
- Cauchy sequence/Short definition
- Chain rule
- Characteristic of a ring
- Characteristic property of the direct product module
- Characteristic property of the direct product module/Statement
- Characteristic property of the direct product module/Statement/Diagram
- Characteristic property of the direct sum module
- Characteristic property of the direct sum module/Statement
- Characteristic property of the direct sum module/Statement/Picture
- Characteristic property of the disjoint union topology
- Characteristic property of the disjoint union topology/Proof
- Characteristic property of the disjoint union topology/Statement
- Characteristic property of the product topology
- Characteristic property of the product topology/Statement
- Characteristic property of the product topology/Statement/Diagram
- Characteristic property of the quotient topology
- Characteristic property of the quotient topology/Statement
- Characteristic property of the subspace topology
- Characteristic property of the subspace topology/Statement
- Characteristic property of the tensor product
- Characteristic property of the tensor product/Statement
- Chart
- Charts
- Circle
- Circular motion
- Circular motion/Notes
- Class of sets closed under complements properties
- Class of sets closed under set-subtraction properties
- Class of smooth real-valued functions on R-n
- Class of smooth real-valued functions on R-n/Structure
- Classes of continuously differentiable functions
- Closed interval
- Closed map
- Closed n-cell
- Closed set
- Closed set in a compact space is compact
- Closed sets
- Closure, interior and boundary
- Closure (set, topology)
- Closure (topology)
- Closure of a set in a topological space
- Co-product (category theory)
- Coarser topology
- Cocone (category theory)
- Combination
- Combinations
- Combinatorics (subject)
- Common data type ranges
- Common integrals table
- Commutative
- Commutativity of intersection
- Commutator
- Commutator subgroup
- Commutivity of intersection
- Compact
- Compact-to-Hausdorff theorem
- Compact (topology)
- Compact set in a Hausdorff space is closed
- Compact subspace of a Hausdorff space is closed
- Compactness
- Compactness/Uniting covers proof
- Comparison test for real series
- Comparison test for real series/Statement
- Complement
- Complementation
- Complete metric space
- Completely invariant under
- Completeness
- Complex conjugate
- Complex functionals
- Composite formula (FOL)
- Composition of continuous maps is continuous
- Composition of functions
- Composition of measurable maps is measurable
- Concatenation of loops and paths (homotopy)
- Concatenation of paths and loops (homotopy)
- Conditional probability
- Conditions for a Dynkin system to be a sigma-algebra
- Conditions for a generated Dynkin system to be a sigma-algebra
- Conditions for a map to be a measurable map
- Cone
- Cone (category theory)
- Cone (topology)
- Cone and cocone compared
- Conjugation
- Connected (topology)
- Connected (topology)/Equivalent conditions
- Connected space
- Connected subset (topology)
- Connected topological space
- Constant function
- Constant loop
- Constant loop based at
- Constant loop based at a point
- Constant map
- Constant mapping
- Continuity
- Continuity and non-surjective functions
- Continuity definitions are equivalent
- Continuous
- Continuous function
- Continuous map
- Continuous map/Claim: continuous iff continuous at every point
- Continuous map/Refactoring tasks
- Continuous maps
- Contractible topological space
- Contrapositive
- Contravariant functor
- Contravariant functor/Definition
- Convergence (sequence)
- Convergence of a sequence
- Convergent (sequence)
- Convergent sequence
- Converges (sequence)
- Convex
- Convex function
- Convex hull
- Convex set
- Coproduct
- Coproduct (category theory)
- Coproduct (module)
- Coproduct (topology)
- Coproduct topology
- Corollary
- Correspondence
- Coset
- Countably additive set function
- Covariant functor
- Covariant functor/Definition
- Covector
- Covector applied to a tensor product
- Cover
- Covering
- Covering map (topology)
- Covering map (topology)/Definition
- Covering space
- Covering space (topology)
- Cu-ring
- Curve
- Cyclic subgroup
- D-system
- DFA
- DFAs
- De Morgan's laws
- Definitions and iff
- Deformation retract
- Deformation retraction
- Deformation retraction/Definition
- Degrees of freedom
- Demonstrating why category arrows are best thought of as arrows and not functions
- Dense
- Dense set
- Derivation
- Derivative
- Derivative (analysis)
- Deriving the exponential distribution from the Poisson distribution
- Deriving the exponential distribution from the time between event in a Poisson distribution
- Deterministic finite acceptor automaton
- Deterministic finite automaton
- Diffeomorphism
- Differentiability
- Differential Geometry
- Differential of a smooth map
- Differentiation
- Differentiation (subject)
- Digraph
- Digraphs
- Dipa/Help
- Direct product (module)
- Direct product module
- Direct product of modules
- Direct sum
- Direct sum (ring)
- Direct sum module
- Directed graph
- Disconnected (topology)
- Disconnected (topology)/Definition
- Disconnected subset (topology)
- Disconnected topological space
- Discrete metric
- Discrete metric and topology
- Discrete metric and topology/Metric space definition
- Discrete metric and topology/Summary
- Discrete topology
- Disjoint
- Disjoint in
- Disjoint in a set
- Disjoint union
- Disjoint union (set)
- Disjoint union (topology)
- Disjoint union space (topology)
- Disjoint union topological space
- Disjoint union topology
- Distance from a point to a set
- Distribution of the sample median