Strongly paracompact space

Definition
A topological space is said to be strongly paracompact if it satisfies the following condition: every open cover has a star-finite open refinement.

Refinement formalism
In the refinement formalism, the property of being strongly paracompact has the following refinement formal expression:

Open $$\to$$ Star-finite open

In other words, every open cover can be refined to a star-finite open cover.

Stronger properties

 * Compact space

Weaker properties

 * Paracompact space