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Weakly compact

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

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Article summary

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

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  1. Summarise the article in your own words. Which single claim would you verify first, and why?
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  3. If two sources disagreed about one of these facts, what would you need in order to trust one over the other?

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