T0 semitopological group

Definition
A semitopological group is said to be $$T_0$$ if it satisfies the following equivalent conditions:


 * 1) The underlying topological space is $$T_0$$ as a topological space i.e. there is no pair of points such that each is in the closure of the other. See T0 space.
 * 2) The underlying topological space is $$T_1$$ i.e. all points are closed. See T1 space.