Sigma-compact 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

Definition

Symbol-free definition

A topological space is said to be sigma-compact or $\sigma$-compact if it has a countable collection of compact subsets such that the union of their interiors is the whole space.

Relation with other properties

Stronger properties

• Hemicompact space
• Compact space
• Manifold