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The Mobius Strip is Not a Smooth Surface
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Topology
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Proof That the Continuous Functions on [0,1] With the Maximum Metric are Second Countable
Proof That the Continuous Image of a Compact Space is Compact
Proof That the Cylinder, Torus and Cube Are Compact Spaces
Proof That the Diagonal Cartesian Product of a Set With Itself is Homeomorphic to the Set
Proof That the Diagonal of a T2 Space is Closed
Proof That the Diameter of a Set Equals the Diameter of its Closure
Proof That The Empty Set, The Set Itself, and the Union and Intersection of Open Sets in a Metric Space Are Open Sets
Proof That The First Countable Property is a Topological Property
Proof That the Graph of a Continuous Function on a Set X is Homeomorphic to X
Proof That the Homeomorphism Relation is Reflexive, Symmetric and Transitive
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