Selective separability in (a)topological spaces

Abstract

In this paper, we study selective versions of separability in (a)topological spaces with the help of some strong and weak forms of open sets. For this we use the notions of semi-closure, pre-closure, ?-closure, ?-closure and ?-closure and their respective density in (a)topological spaces. The interrelationships between different types of selective versions of separability in (a)topological spaces have been given by suitable counterexamples. Sufficient conditions are given for (a)topological spaces to be (a)Rt-separable and (a)Mt-separable for each t ? {s, p, ?, ?, ?}. It is shown that under some condition (a)Mt-separability and (a)Rt-separability are equivalent.