paracompact topological space

A topological spaceMathworldPlanetmath X is said to be paracompact if every open cover of X has a locally finitePlanetmathPlanetmath open refinement.

In more detail, if (Ui)iI is any family of open subsets of X such that


then there exists another family (Vi)iI of open sets such that

ViUi for all iI

and any specific xX is in Vi for only finitely many i.

Some properties:

Title paracompact topological space
Canonical name ParacompactTopologicalSpace
Date of creation 2013-03-22 12:12:47
Last modified on 2013-03-22 12:12:47
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 9
Author mathcam (2727)
Entry type Definition
Classification msc 54-00
Classification msc 55-00
Synonym paracompact space
Related topic ExampleOfParacompactTopologicalSpaces
Defines paracompact
Defines paracompactness