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About: Compact group     Goto   Sponge   Distinct   Permalink

An Entity of Type : dbo:Band, within Data Space : dbpedia.org associated with source document(s)

Type: Thingyago:WikicatLieGroupsyago:WikicatTopologicalGroupsyago:Abstraction100002137yago:Group100031264Band New Facet based on Instances of this Class

In mathematics, a compact (topological) group is a topological group whose topology realizes it as a compact topological space (when an element of the group is operated on, the result is also within the group). Compact groups are a natural generalization of finite groups with the discrete topology and have properties that carry over in significant fashion. Compact groups have a well-understood theory, in relation to group actions and representation theory. In the following we will assume all groups are Hausdorff spaces.