# Compact group

From Groupprops

This article defines a property that can be evaluated for a topological group (usually, a T0 topological group)

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This article gives a basic definition in the following area: topological group theory

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## Definition

### Symbol-free definition

A topological group is said to be **compact** if its underlying topological space is a compact space; in other words, if every open cover of the group has a finite subcover.