Topological Group

A continuous group G which has the topology of a T2-space is a topological group. The simplest example is the group of real numbers under addition.

The homeomorphism group of any compact T2-space is a topological group when given the compact-open topology. Also, any Lie group is a topological group.

See also

Effective Action, Free Action, Group, Group Orbit, Group Representation, Isotropy Group, Matrix Group, Quotient Space, Transitive

This entry contributed by Todd Rowland

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Rowland, Todd. "Topological Group." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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