Weakly compact can refer to:
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Weakly compact cardinal, an infinite cardinal number on which every binary relation has an equally large homogeneous subset
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Weakly compact set, a compact set in a space with the weak topology
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Weakly compact set, a set that has some but not all of the properties of , for example:
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Sequentially compact space, a set in which every infinite sequence has a convergent subsequence
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Limit point compact, a set in which every infinite subset of X has a limit point
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