# Pages that link to "If and only if"

From Maths

The following pages link to **If and only if**:

- Quotient topology (← links)
- The set of all open balls of a metric space are able to generate a topology and are a basis for that topology (← links)
- Product topology (← links)
- Bounded set (← links)
- A collection of subsets is a sigma-algebra iff it is a Dynkin system and closed under finite intersections (← links)
- 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 (← links)
- Basis for a topology (← links)
- Template:Iff (← links)
- Continuous map/Claim: continuous iff continuous at every point (← links)
- Notes:Continuous at a point (← links)
- Infimum (← links)
- Characteristic property of the quotient topology (← links)
- Characteristic property of the product topology (← links)
- Characteristic property of the product topology/Statement (← links)
- Disjoint union topology (← links)
- Notes:Connected space (← links)
- Notes:Basis for a topology (← links)
- Notes:Basis for a topology/Attempt 2 (← links)
- Task:Characteristic property of the subspace topology (← links)
- Task:Characteristic property of the coproduct topology (← links)
- Notes:Advanced Linear Algebra - Roman/Chapter 2 (← links)
- Notes:Basis for a topology/McCarty (← links)
- A subset of a topological space is open if and only if it is a neighbourhood to all of its points (← links)
- Template:Amcm (← links)
- First order language (← links)
- Notes:Quotient topology/Table (← links)
- Topology generated by a basis/Statement (← links)
- Topology generated by a basis (← links)
- Characteristic property of the disjoint union topology/Statement (← links)
- Characteristic property of the disjoint union topology (← links)
- Closed map (← links)
- Dense (← links)
- Equivalent statements to a set being dense (← links)
- A set is dense if and only if every non-empty open subset contains a point of it (← links)
- 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 (← links)
- 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 (← links)
- A topological space is disconnected if and only if it is homeomorphic to a disjoint union of two or more non-empty topological spaces (← links)
- 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 (← links)
- 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 (← links)
- Exercises:Mond - Topology - 1 (← links)
- Characteristic property of the quotient topology/Statement (← links)
- Factoring a continuous map through the projection of an equivalence relation induced by that map yields an injective continuous map (← links)
- Exercises:Mond - Topology - 1/Question 9 (← links)
- A map is continuous if and only if the pre-image of every closed set is closed (← links)
- 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 (← links)
- A set is open if and only if every point in the set has an open neighbourhood contained within the set (← links)
- Definitions and iff (← links)
- Equivalent conditions to a set being saturated with respect to a function (← links)
- Equivalent conditions to a map being a quotient map (← links)
- Exercises:Rings and Modules - 2016 - 1 (← links)