Paracompact space

This article defines a property of topological space that is pivotal (viz important) among currently studied properties of topological spaces

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

Definition

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

Relation with other properties

Stronger properties

• Compact space
• Paracompact manifold
• Paracompact Hausdorff space
• Regular Lindelof space
• Metrizable space

Weaker properties

• Metacompact space
• Orthocompact space
• Locally paracompact space