Compact = Closed + Bounded + (?)

real-analysis soft-question

Solution 1:

For Banach spaces, there is a big table in Dunford & Schwartz characterizing compactness of subsets in many different spaces.

Zev is right that "complete + totally bounded" is the general formulation. For subset in Banach space, complete holds if and only if closed. So the question is to characterize total boundedness.

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