Compact group: Difference between revisions

From Groupprops
No edit summary
 
(One intermediate revision by one other user not shown)
Line 12: Line 12:


* [[Compact implies every open subgroup has finite index]]
* [[Compact implies every open subgroup has finite index]]
* [[Compact and connected implies no proper open or closed subgroup of finite index]]
* [[Complex representation of compact group is unitary]]

Latest revision as of 19:07, 15 January 2024

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.

Facts