# Strongly paracompact space

From Topospaces

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

## Contents

## 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 Star-finite open

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