Strongly paracompact space

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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

Weaker properties