Selective version of star-semi-Lindel\"{o}fness in $(a)$topological spaces

Abstract

In this paper, we concerned with the properties $(a)R$-star-semi-Lindel\"{o}f and $(a)M$-star-semi-Lindel\"{o}f in $(a)$topological spaces. These properties are interesting as every $(a)R^s$-separable space is $(a)R$-star-semi-Lindel\"{o}f and every $(a)^s$-semi-Lindel\"{o}f space is $(a)R$-star-semi-Lindel\"{o}f but not every $(a)R$-star-semi-Lindel\"{o}f space is $(a)R^s$-separable or $(a)^s$-semi-Lindel\"{o}f. It is shown that if an $(a)$topological space $X$ is the union of countably many $(a)$-open and $(a)R$-star-semi-Lindel\"{o}f subspaces, then $X$ is $(a)R$-star-semi-Lindel\"{o}f. Similar results are obtained in the context of $(a)M$-star-semi-Lindel\"{o}f spaces. Further, suitable and required counterexamples are given.