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Proof That the Only Topology on a Finite Set X Which Makes X a T1 Space is the Discrete Topology
Proof That the Open Interval (0,1) is Not Countably Compact
Proof That the Plane With the Euclidean Metric is Locally Compact
Proof That the Plane With the Usual Topology is Second Countable
Proof That The Property of Being Homotopic is an Equivalence Relation
Proof That the Quotient of the Set of Cauchy Sequences in a Metric Space is a Completion of the Metric Space
Proof That the Quotient Topology is a Topology
Proof That the Rational Numbers are Not Locally Compact With the Euclidean Topology
Proof That the Rational Numbers With the Euclidean Topology is Totally Disconnected
Proof That the Real Numbers Are a Completion of the Set of Rational Numbers
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