Relativization of Star-C-Hurewicz Property in Topological Spaces

Abstract

In this paper, we introduced relatively star-C-Hurewicz property in topological spaces following the approach of Bonanzinga and Pansera (Acta Math Hungar 117(3):231–243, 2007) and Guido and Kočinac (Quest Answ Gen Topol 19:107–114, 2001). A subspace A of a topological space X is said to have relatively star-C-Hurewicz property in X (in short, RSCH) or relatively star-C-Hurewicz subspace of X if for each sequence $\left<{\mathcal {U}}_n : n \in \omega \right>$ of open covers of X there is a sequence $\left<A_n : n \in \omega \right>$ of countably compact subsets of X such that $x \in A$ belongs to $St(A_n, {\mathcal {U}}_n)$ for all but finitely many n. It is shown that relatively star-C-Hurewicz property is hereditary. In this manner, we obtained relationships of relatively star-C-Hurewicz property with other existing Hurewicz properties in the literature.