Page "Topological group" Paragraph 21

Every subgroup of a topological group is itself a topological group when given the subspace topology.

If H is a subgroup of G, the set of left or right cosets G / H is a topological space when given the quotient topology ( the finest topology on G / H which makes the natural projection q: G → G / H continuous ).

One can show that the quotient map q: G → G / H is always open.