Almost Menger and related spaces

Abstract

In this paper we consider the notion of almost Menger property whichis similar to the familiar property of Menger and prove that we canuse regular open sets instead of open sets in the definition ofalmost Menger property. We give conditions for a space $X^n$ to bealmost Menger. In the similar way, we consider almost $\gamma$-setsand the almost star-Menger property.