The set of left cosets of a subgroup H of a topological group G forms a topological space. Its topology is defined by the quotient topology from π:G->G/H. Namely, the open sets in G/H are the images of the open sets in G. Moreover, if H is closed, then G/H is a T_2-space.

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

Marius Sophus Lie