Abstract

A topological space $X$ is called $G_{\delta}$-selectively (resp., $SG_{\delta}$-selectively) separable if for every sequence $\left( D_{n}: n\in\omega\right) $ 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.

Keywords: Selectively separable; $R$-separable; $G_{\delta}$-selectively separable; $SG_{\delta}$-selectively separable.

MSC: 54C35, 54D65, 54E65

Pages:  168$-$173     

Volume  73 ,  Issue  3 ,  2021