User:Leigh.Samphier/Topology

Topology

 * User:Leigh.Samphier/Topology/Definition:Open Discrete Set of Subsets


 * 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/Precise Refinement of Sigma-Discrete Cover is Sigma-Discrete

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

User:Leigh.Samphier/Topology/Common Refinement Condition for Open Sigma-Discrete Refinement of Open Cover


 * User:Leigh.Samphier/Topology/Discrete Set of Subsets is Locally Finite


 * User:Leigh.Samphier/Topology/Sigma-Discrete Set of Subsets is Sigma-Locally Finite


 * User:Leigh.Samphier/Topology/Refinement of a Refinement is Refinement of Cover


 * User:Leigh.Samphier/Topology/Sigma-Locally Finite Cover and Countable Locally Finite Cover have Common Locally Finite Refinement


 * User:Leigh.Samphier/Topology/Sigma-Locally Finite Cover has Locally Finite Refinement


 * User:Leigh.Samphier/Topology/Sigma-Locally Finite Cover has Locally Finite Refinement/Lemma 1


 * User:Leigh.Samphier/Topology/Sigma-Locally Finite Cover has Locally Finite Refinement/Lemma 2


 * User:Leigh.Samphier/Topology/Locally Finite Set of Subsets is Sigma-Locally Finite Set of Subsets

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 1 implies Statement 6


 * 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/Characterization of Paracompactness in T3 Space/Lemma 7


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

User:Leigh.Samphier/Topology/Definition:Star (Topology)

User:Leigh.Samphier/Topology/Definition:Star Refinement

User:Leigh.Samphier/Topology/Definition:Barycentric Refinement

User:Leigh.Samphier/Topology/Fully T4 Space is T4 Space

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

User:Leigh.Samphier/Topology/Discrete Space is Fully T4

User:Leigh.Samphier/Topology/Metric Space is Fully T4

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

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

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Statement n implies Statement 7

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Statement 7 implies Statement n

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

User:Leigh.Samphier/Topology/T1 Space is Fully T4 iff Paracompact

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