On the Alster, Menger and D-type covering properties

Abstract

In this paper we give new characterizations for almost Menger and weakly Menger spaces by neighborhood assignments and dene a natural weakening of almost D-spaces and weakly D-spaces. We discuss the relationships among the properties "D-type", "Menger", "Alster", and the weak versions of these properties in Lindelof spaces.

Key words: Menger spaces, almost Menger spaces, weakly Menger spaces, D-spaces, Alster spaces, almost Alster spaces, selection principles, topological games.