User:Leigh.Samphier/Topology

Topology
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/Subset of Cover is Cover of Subset

User:Leigh.Samphier/Topology/Precise Refinement of Locally Finite Cover is Locally Finite

User:Leigh.Samphier/Topology/Common Refinement Condition for Open Locally Finite Refinement of Open Cover

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 1

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/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/Characterization of Paracompactness in T3 Space/Lemma 4

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Lemma 5

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Lemma 6

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/T1 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