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Proof That if a Countable Local Base Exists at a Point of a Topological Set Then a Nested Local Base Exists at the Point
Proof That if a Space Has a Finite Number of Components Then Each Component is Open
Proof That if a T0 or T1 Space is Homeomorphic to Another Space, That Space is T0 or T1 Respectively
Proof That if Any Two Points in a Space are in a Connected Set, Then the Set is Connected
Proof That if the Class of Real Valued Continuous Functions Separates Points of a Space Then That Space is Hausdorff
Proof That if the Domain is a T2 Space and a Function is Onto and One to One, and the Inverse Function is Continuous, then the Codomain is a T2 Space
Proof That if the Quotient Space of the Cauchy Sequences in a Metric Space is a Completion of a Metric Space, then The Quotient Space is Isomorphic to That Space
Proof That in a Hausdorff Space Every Convergent Sequence Has a Unique Limit
Proof That in Euclidean Space There are Sets That are Not Borel Sets
Proof That Open Sets Defined By Inverse Functions Constitute a Topology
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