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单词 LocallyCompact
释义

locally compact


A topological spaceMathworldPlanetmath X is locally compact at a point xX if there exists a compact set K which contains a nonempty neighborhoodMathworldPlanetmathPlanetmath U of x. The space X is locally compact if it is locally compact at every point xX.

Note that local compactness at x does not require that x have a neighborhood which is actually compact, since compact open sets are fairly rare and the more relaxed condition turns out to be more useful in practice. However, it is true that a space is locally compact at x if and only if x has a precompact neighborhood.

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更新时间:2025/5/4 11:44:32