Strongly paracompact space

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

This is a variation of compactness. View other variations of compactness

This is a variation of paracompactness. View other variations of paracompactness

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.

Formalisms

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.

Relation with other properties

Stronger properties

• Compact space

Weaker properties

• Paracompact space