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).

Title locally closed
Canonical name LocallyClosed
Date of creation 2013-03-22 17:36:12
Last modified on 2013-03-22 17:36:12
Owner asteroid (17536)
Last modified by asteroid (17536)
Numerical id 5
Author asteroid (17536)
Entry type Definition
Classification msc 54D99