SGδ-SELECTIVE SEPARABILITY

Abstract

A topological space $X$ is called $G_{\delta }$-selectively (resp., $S{G}_{\delta }$-selectively) separable if for every sequence $(D_n:n\in \omega )$ of dense $G_{\delta }$ subsets of $X$, one can pick finite subsets $F_n\subset D_n$ such that $\bigcup _{n\in \omega }{F}_n$ is dense (resp., dense and $G_{\delta }$). In this paper we introduce and study these kinds of spaces.