User:Leigh.Samphier/Topology

Topology

 * Subset of Locally Finite Set of Subsets is Locally Finite


 * Subset of Sigma-Locally Finite Set of Subsets is Sigma-Locally Finite


 * Countable Open Covers Condition for Separated Sets


 * Countable Open Covers Condition for Separated Sets/Lemma 1


 * Countable Open Covers Condition for Separated Sets/Lemma 2


 * Characterization of Open Set by Open Cover

User:Leigh.Samphier/Topology/Characterization of Closed Set by Open Cover

User:Leigh.Samphier/Topology/Template:Closed-set-axiom

User:Leigh.Samphier/Topology/Union of Closed Locally Finite Set of Subsets is Closed

User:Leigh.Samphier/Topology/Closures of Elements of Locally Finite Set is Locally Finite

User:Leigh.Samphier/Topology/Union of Closures of Elements of Locally Finite Set is Closed

User:Leigh.Samphier/Topology/Set is Neighborhood of Subset iff Neighborhood of all Points of Subset

User:Leigh.Samphier/Topology/Open Cover with Closed Locally Finite Refinement is Even Cover

User:Leigh.Samphier/Topology/Open Cover with Closed Locally Finite Refinement is Even Cover/Lemma 1

User:Leigh.Samphier/Topology/Open Cover with Closed Locally Finite Refinement is Even Cover/Lemma 2

User:Leigh.Samphier/Topology/Open Cover with Closed Locally Finite Refinement is Even Cover/Lemma 3

User:Leigh.Samphier/Topology/Open Cover with Closed Locally Finite Refinement is Even Cover/Lemma 4

User:Leigh.Samphier/Topology/Open Covers with Common Refinement have Common Open Refinement Between

User:Leigh.Samphier/Topology/Set of all Singletons is Refinement of Cover

User:Leigh.Samphier/Topology/Open Covers have Common Refinement

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Statement 1 implies Statement 2

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Statement 2 implies Statement 3

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Statement 3 implies Statement 4

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Statement 4 implies Statement 5

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Statement 5 implies Statement 6

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Statement 6 implies Statement 2

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Statement 2 implies Statement 1

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Lemma 1

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Lemma 2

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Lemma 3

User:Leigh.Samphier/Topology/T3 Space with Sigma-Locally Finite Basis is Paracompact

User:Leigh.Samphier/Topology/T3 Space is Fully T4 iff Paracompact

User:Leigh.Samphier/Topology/T3 Space with Sigma-Locally Finite Basis is T4 Space

User:Leigh.Samphier/Topology/T3 Space with Sigma-Locally Finite Basis is T4 Space/Proof 1

User:Leigh.Samphier/Topology/T3 Space with Sigma-Locally Finite Basis is T4 Space/Proof 2

User:Leigh.Samphier/Topology/T3 Space with Sigma-Locally Finite Basis is T4 Space/Lemma 1

User:Leigh.Samphier/Topology/T3 Space with Sigma-Locally Finite Basis is T4 Space/Lemma 2

User:Leigh.Samphier/Topology/Regular Space with Sigma-Locally Finite Basis is Normal Space


 * User:Leigh.Samphier/Topology/Nagata-Smirnov Metrization Theorem

User:Leigh.Samphier/Topology/Nagata-Smirnov Metrization Theorem/Necessary Condition

User:Leigh.Samphier/Topology/Nagata-Smirnov Metrization Theorem/Sufficient Condition

Possible inclusions
User:Leigh.Samphier/Topology/Characterization of Paracompact Space by Precise Refinement

User:Leigh.Samphier/Topology/Paracompact T2 Space is T3 Space

User:Leigh.Samphier/Topology/Paracompact T2 Space is Regular

User:Leigh.Samphier/Topology/Paracompact T2 Space is T4 Space

User:Leigh.Samphier/Topology/Paracompact T2 Space is Normal

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T4 Space


 * Bing's Metrization Theorem


 * Smirnov Metrization Theorem


 * Frink's Metrization Theorem


 * Stone-Weierstrass Theorem


 * Stone-Cech Compactification


 * Stone's Representation Theorem for Boolean Algebras


 * Jordan Curve Theorem