Open subgroup

Definition
A subgroup of a semitopological group is termed an open subgroup if it is an open subset in the subspace topology.

Stronger properties

 * Closed subgroup of finite index

Weaker properties

 * Closed subgroup

Facts

 * All cosets of an open subgroup are open. Thus, in a connected topological group, there cannot exist any proper open subgroup.
 * In a compact group, any open subgroup must have finite index