strongly paracompact space

A collectionMathworldPlanetmath 𝒜 of sets is said to be star-finite if each member of 𝒜 meets only finitely many members of 𝒜.

A topological spaceMathworldPlanetmath X is said to be strongly paracompact if every open cover of X has a star-finite open refinement.

A star-finite open cover of a topological space is clearly locally finitePlanetmathPlanetmath. Therefore, every strongly paracompact space is paracompact (as the name suggests).

Title strongly paracompact space
Canonical name StronglyParacompactSpace
Date of creation 2013-03-22 17:09:01
Last modified on 2013-03-22 17:09:01
Owner yark (2760)
Last modified by yark (2760)
Numerical id 5
Author yark (2760)
Entry type Definition
Classification msc 54D20
Synonym strongly paracompact topological space
Defines strongly paracompact
Defines star-finite
Defines star finite