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 define 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 Lindelöf spaces.

Mathematics Subject Classification (2010):

• 54D20
• 54G99
• 54D10

Key words:

• Menger spaces
• almost Menger spaces
• weakly Menger spaces
• D-spaces
• Alster spaces
• almost Alster spaces
• selection principles
• topological games