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

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Advance Math

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

(a) A convergent sequence is bounded.

(b) The limit of a sequence is unique.

(c) A n -neighborhood is an open set.

(d) A finite union of open sets is open.

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

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

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