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Real Analysis : Bounded Open Balls

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Show that a set E in the metric space X is bounded if and only if, for some "a" in X, there exists an open ball B(a;r) such that E is a subset of B(a;r).

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Bounded open balls are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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Proof:

It is clear that B[a;r] is just a fancy way of denoting the ...

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