Topological group

In mathematics, a topological group G is a group that is also a topological space such that the group multiplication G × G → G and the inverse operation G → G are continuous maps. Here, G × G is viewed as a topological space by using the product topology. Although we do not do so here, it is common to also require that the topology on G be Hausdorff, namely that any two points in this space have disjoint neighborhoods. The reasons, and some equivalent conditions, are discussed below. In the language of category theory, one would say that topological groups are group objects in the category of topological spaces.

Related Topics:
Mathematics - Group - Topological space - Continuous - Product topology - Hausdorff - Neighborhoods - Group object - Category of topological spaces

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Almost all objects investigated in analysis are topological groups (usually with some additional structure).

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