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Proof That the Union of a Set and its Boundary Equals the Closure of the Set
Proof That the Union of Any Family of Connected Subsets of Any Space Having at Least One Point in Common is Also Connected
Proof That the Union of Two Connected Sets Not Mutually Separated are Connected
Proof That There is No Continuous Function From a Connected Space Onto The Set {0,1} With the Discrete Topology
Proof That Totally Bounded Sets Are Bounded
Proof That Two Loops Can Be Joined to Make a New Loop
Proof That Union and Intersection of Subsets of a Set X Open in X Are a Topology for X
Proof That Union of Two Continua is a Continuum
Proof That Urysohn's Lemma is a Special Case of Tietze's Extension Theorem
Properties of Closed Sets
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