On star-C-menger spaces

Abstract

A space X is star-C-Menger if for each sequence (U_n : n ∈ N) of open covers of X there exists a sequence (Ksub>n : n ∈ N) of countably compact subsets of X such that {St(K_n; U_n) : n ∈ N} is an open cover of X. In this paper, we investigate the relationship between star-C-Menger spaces and related spaces, and study topological properties of star-<C-Menger spaces.

Keywords: Selection principles, star-Menger, star-K-Menger, star-C-Menger, star-L-Menger, starcompact, star-Lindelof, starcompact, star-L-Lindelof.

Quaestiones Mathematicae 37(2014), 337-347.