# strongly paracompact space

A collection $\mathcal{A}$ of sets is said to be star-finite if each member of $\mathcal{A}$ meets only finitely many members of $\mathcal{A}$.

A topological space $X$ 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 finite. Therefore, every strongly paracompact space is paracompact (as the name suggests).

Title strongly paracompact space StronglyParacompactSpace 2013-03-22 17:09:01 2013-03-22 17:09:01 yark (2760) yark (2760) 5 yark (2760) Definition msc 54D20 strongly paracompact topological space strongly paracompact star-finite star finite