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For example, in R, the closed unit interval [0, 1] is compact, but the set of integers Z is not (it is not bounded) and neither is the half-open interval [0, 1) (it is not closed).
Compact space, a closed and bounded subset of an Euclidean space.
Compactness theorem, a set of first-order sentences is satisfiable if every finite subset of it is satisfiable.
Compact element, those elements of a partially ordered set that cannot be subsumed by a supremum of any directed set that does not already contain them.
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