Compact group: Difference between revisions

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===Symbol-free definition===
===Symbol-free definition===


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

Revision as of 19:14, 24 December 2007

This article defines a property that can be evaluated for a topological group (usually, a T0 topological group)
View a complete list of such properties


This article gives a basic definition in the following area: topological group theory
View other basic definitions in topological group theory |View terms related to topological group theory |View facts related to topological group theory

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.