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

This property is a pivotal (important) member of its property space. Its variations, opposites, and other properties related to it and defined using it are often studied

Category:Variations of paracompactness

Stronger properties

• Compact space
• Hereditarily paracompact space
• Strongly paracompact space
• Paracompact Hausdorff space
• Regular Lindelof space
• Metrizable space

Weaker properties

• Metacompact space
• Orthocompact space
• Locally paracompact space