User:Leigh.Samphier/Topology

Topology
User:Leigh.Samphier/Topology/Homeomorphic Image of Sub-Basis is Sub-Basis

User:Leigh.Samphier/Topology/Homeomorphic Topology of Initial Topology is Initial Topology

User:Leigh.Samphier/Topology/Definition:Evaluation Mapping (Topology)

User:Leigh.Samphier/Topology/Composite of Evaluation Mapping and Projection

User:Leigh.Samphier/Topology/Every Topological Evaluation Mapping is Continuous

User:Leigh.Samphier/Topology/Subspace of Product Space has Initial Topology with respect to Restricted Projections

User:Leigh.Samphier/Topology/Definition:Mappings Separating Points

User:Leigh.Samphier/Topology/Definition:Mappings Separating Points from Closed Sets

User:Leigh.Samphier/Topology/Evaluation Map is Injective iff Mappings Separate Points

User:Leigh.Samphier/Topology/Injection is Open Mapping iff Image of Sub-Basis Set is Open

User:Leigh.Samphier/Topology/Characterization for Topological Evaluation Mapping to be Embedding

User:Leigh.Samphier/Topology/Characterization for Topological Evaluation Mapping to be Embedding/Necessary Condition

User:Leigh.Samphier/Topology/Characterization for Topological Evaluation Mapping to be Embedding/Sufficient Condition

User:Leigh.Samphier/Topology/Characterization for Continuous Mappings Separate Points from Closed Sets

User:Leigh.Samphier/Topology/Evaluation Mapping on T1 Space is Embedding iff Separates Points from Closed Sets

User:Leigh.Samphier/Topology/Regular Second-Countable Space is Homeomorphic to Subspace of Hilbert Cube

User:Leigh.Samphier/Topology/Regular Second-Countable Space is Homeomorphic to Subspace of Hilbert Cube/Lemma 1

User:Leigh.Samphier/Topology/Regular Second-Countable Space is Homeomorphic to Subspace of Hilbert Cube/Lemma 2


 * Urysohn's Metrization Theorem

User:Leigh.Samphier/Topology/Subspace of Metrizable Space is Metrizable Soace

User:Leigh.Samphier/Topology/Topological Space Homeomorphic to Metrizable Space is Metrizable Soace

User:Leigh.Samphier/Topology/Urysohn's Metrization Theorem


 * Metrization of Regular Second Countable Space


 * Nagata-Smirnov Metrization Theorem


 * Bing's Metrization Theorem


 * Smirnov Metrization Theorem


 * Frink's Metrization Theorem