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单词 LocallyClosed
释义

locally closed


- A subset Y of a topological spaceMathworldPlanetmath X is said to be locally closed if it is the intersectionMathworldPlanetmath of an open and a closed subset.

The following result provides some definitions:

- The following are equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath:

  1. 1.

    Y is locally closed in X.

  2. 2.

    Each point in Y has an open neighborhood UX such that UY is closed in U (with the subspace topology).

  3. 3.

    Y is open in its closureMathworldPlanetmathPlanetmath Y¯ (with the subspace topology).

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更新时间:2025/5/4 11:21:56