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Question: topology topology question please write clearly i dont need a...

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Topology

Theorem If X is a metric space with induced topology T, then (X,T) is Hausdorff. The contrapositive of this theorem must be true: If (X,T) is not Hausdorff, then X is not a metric space 1) Consider (R,T) with the topology induced by the taxicab metric. Using the definition for Hausdorff, give an example of why (R,T) is Hausdorff. 2) The finite complement topology on R is not Hausdorff. Explain why R with the finite complement topology is non- metrizable

Topology Question

Please write clearly. I don't need a long explanation just one that makes sense.

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