Supply proofs for the following miscellaneous propositions from the course in a metric space context: (1) A...

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Supply proofs for the following miscellaneous propositions fromthe course in a metric space context:

(1) A compact set (you may use either definition) is closed andbounded.

(2) An epsilon-neighborhood is an open set.

(3) A set is open if and only if its complement is closed.

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