Compact group

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.

Facts

• Compact implies every open subgroup has finite index
• Complex representation of compact group is unitary