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Proof That a Nested Local Base at a Point of a Topological Space Contains a Sequence Converging to the Point
Proof That a Non Constant Continuous Function Exists on a T4 Space Containing More Than One Point
Proof That a One to One Continuous Function From a Compact Space into a Hausdorff Space is a Homeomorphism
Proof That a Path Connected Set is Connected
Proof That a Product of Connected Spaces is Connected
Proof That a Pseudometric Space is Not T0
Proof That a Second Countable Space is Separable
Proof That a Separable Metric Space is Homeomorphic to a Dense Subspace of a Complete Metric Space
Proof That a Sequentially Compact Space is Countably Compact
Proof That a Sequentially Compact Subset of a Metric Space is Compact

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