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Proof That Any Connected Subset of a Set Consisting of Disjoint Open Subsets Must be Contained in One of Those Subsets
Proof That any Element in the Complement of a Compact Subset of a Hausdorff Space is in a Open Subset of the Complement
Proof That Any Element Not in a Compact Subset of a Hausdorff Space is in an Open Set That Has No Intersection With an Open Set Containing the Compact Subset
Proof That Any Open Connected Subset of Rn is Polygonally Connected
Proof That Any Open Subspace of a Separable Space is Separable
Proof That Any Topological Space With the Indiscrete Topology Containing More Than One Point is Normal
Proof That Any Two Paths in the Plane are Homotopic
Proof That Any Two Points of a T1 Space Are in Open Sets Not Containing the Other Point
Proof That Associativity is Preserved on Homotopy Classes
Proof That Being a T4 Space is a Topological Property

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