A continuous group G which has the topology of a T_2-space is a topological group. The simplest example is the group of real numbers under addition. The homeomorphism group of any compact T_2-space is a topological group when given the compact-open topology. Also, any Lie group is a topological group.

effective action | free action | group | group orbit | group representation | isotropy group | matrix group | quotient space | transitive