T0 quasitopological group

Definition

A quasitopological 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.