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

iIUi=X,

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

iIVi=X
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