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Proof That The Homotopy Property is Reflexive
Proof That The Homotopy Property With Given Base Point is an Equivalence Relation
Proof That The Identity Function is Continuous if and only if the Destination Topology is Finer Than The Source Topology
Proof That the Identity Function On the Unit Disc is Homotopic to the Constant Function Mapping the Disk to the Origin
Proof That the Intersection of a Closed Set With a Compact Set is Compact
Proof That the Interval (0,1) is Not Compact With the Absolute Value Topology
Proof That the Line and the Plane Are Not Homeomorphic
Proof That the Metric on the Quotient Space of Cauchy Sequences is Well Defined
Proof That The Only Connected Subsets of the Real Numbers With the Euclidean Topology Having More Than One Point are the Intervals and the Real Numbers
Proof That the Only Open Subsets Open in a Connected Set are the Set and the Empty Set

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