User:Leigh.Samphier/Topology

Topology

 * Characterization of Neighborhood by Basis


 * Definition:Open Discrete Set of Subsets


 * Composition of Symmetric Relation with Itself is Union of Products of Images


 * Inverse of Neighborhood of Diagonal Point is Neighborhood


 * Intersection of Neighborhood of Diagonal with Inverse is Neighborhood


 * Characterization of Set Equals Union of Sets


 * Subset of Discrete Set of Subsets is Discrete


 * Composition of Relations Preserves Subsets


 * Set of Images of Reflexive Relation is Cover of Set


 * Image of Element under Cartesian Product of Subsets


 * Corollary to Image under Subset of Relation is Subset of Image under Relation


 * Image of Point under Neighborhood of Diagonal is Neighborhood of Point


 * Image of Subset under Neighborhood of Diagonal is Neighborhood of Subset


 * Image under Left-Total Relation is Empty iff Subset is Empty


 * Image of Subset under Composite Relation


 * Image of Element under Composite Relation


 * Image of Subset under Composite Relation with Common Codomain and Domain


 * Image of Element under Composite Relation with Common Codomain and Domain


 * User:Leigh.Samphier/Topology/Characterization of Even Cover


 * User:Leigh.Samphier/Topology/Inverse of Open Set in Product Space is Open in Inverse Product Space


 * User:Leigh.Samphier/Topology/Image of Point under Open Neighborhood of Diagonal is Open Neighborhood of Point


 * User:Leigh.Samphier/Topology/Image of Subset under Open Neighborhood of Diagonal is Open Neighborhood of Subset


 * 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/Characterization of Paracompactness in T3 Space/Lemma 8

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Lemma 9

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Lemma 10


 * User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Lemma 11


 * User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Lemma 12

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Lemma 13

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Lemma 14

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Lemma 15

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Lemma 16

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Lemma 17

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Lemma 18

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Lemma 19

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Lemma 20

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Lemma 21

User:Leigh.Samphier/Topology/Characterization of Paracompactness in T3 Space/Lemma 22


 * 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/T3 Space with Sigma-Locally Finite Basis is Perfectly T4 Space


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


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


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