Question 10 (418)

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

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