Limit point compact

In mathematics, a topological space X is said to be limit point compact[1] or weakly countably compact if every infinite subset of X has a limit point in X. This property generalizes a property of compact spaces. In a metric space, limit point compactness, compactness, and sequential compactness are all equivalent. For general topological spaces, however, these three notions of compactness are not equivalent.

Properties and Examples

See also

Notes

  1. The terminology "limit point compact" appears in a topology textbook by James Munkres, and is apparently due to him. According to him, some call the property "Fréchet compactness", while others call it the "Bolzano-Weierstrass property". Munkres, p. 178179.

References


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