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.