strongly paracompact space

A collection $𝒜$ of sets is said to be star-finiteif each member of $𝒜$meets only finitely many members of $𝒜$.

A topological space $X$ is said to be strongly paracompactif every open cover of $X$ has a star-finite open refinement.

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