SELECTIVE SEPARABILITY IN $(a)$TOPOLOGICAL SPACES

Abstract

In this paper, we study selective version of separability in $(a)$topol-\\ogical spaces with the help of some strong and weak form of open sets. For this we use the notion of semi-closure, pre-closure, $\alpha$-closure, $\beta$-closure and $\delta$-closure and their respective density in $(a)$topological spaces. The interrelationship between different types of selective version of separability in $(a)$topological spaces has been given by suitable counterexamples. Sufficient conditions are given for $(a)$spaces to be $(a)R^t$-separable and $(a)M^t$-separable for each $t\in\{s,p,\alpha,\beta,\delta\}$. It is shown that under some condition $(a)M^t$-separability and $(a)R^t$-separability are equivalent.