Suppose \(\Gamma\) is a subgroup of a topological group \(G\). An orbit of the right action of \(\Gamma\) on \(G\) is of the form \(\{g\gamma\mid \gamma \in \Gamma\}\) which is precisely the left coset \(g\Gamma\).
The corresponding orbit space is the left coset space \(\Gamma/G\) with quotient topology. It is called coset space.
Remarks
- Unfortunately, the right action produces the left coset space and vice versa.