Topology

Articles
Title
Proof That a Set With the Order Topology is a T2 Space
Proof That a Space Containing a Connected Dense Subspace is Connected
Proof That a Space With the Discrete Topology is Totally Disconnected and Locally Connected
Proof That a Subsequence of a Cauchy Sequence is Cauchy
Proof That a Subset of a Completely Regular Space is Completely Regular
Proof That a Subset of a T4 Space Gives Rise to a T4 Space
Proof That a Subspace is Connected if and Only if it Cannot Be Expressed as the Union of Nonempty, Mutually Separated Subsets
Proof That a Subspace of a First Countable Set is First Countable
Proof That a Topological Space is Regular if and Only Every Element is in an Open Set That Has a Closed Subset Containing the Element
Proof That a Topological Space With the Cofinite Topology is Compact

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