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Proof That Every Subspace of a Regular Space is Regular
Proof That Every Subspace of a Second Countable Space is Second Countable
Proof That Every T2 Space is a T1 Space
Proof That Every T3 Space is Also a T2 Space
Proof That Every T4 Space is Also a T3 Space
Proof That for a Closed Function the Closure of an Image Set is a Subset of the Image of the Closure and Vice Versa
Proof That For a Nowhere Dense Subset of a Metric Space and an Open Set U, An Open Subset of U exists With No Intersection With the Nowhere Dense Subset
Proof That for all Continuous Functions the Image of a Closed Set is a Subset of the Closure of the Image
Proof That Homeomorphisms Preserve The Continuum Property
Proof That Homotopy Mappings of Homotopic Functions Are Homotopic

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