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 | 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== | |||
* [[Compact implies every open subgroup has 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.