Some counterexamples and properties on generalizations of Lindelöf spaces

Abstract

In this paper we give some significative counterexamples to prove that some well known generalizations of Lindelöf property are proper. Also we give some new results, we introduce and study the almost regular-Lindelof spaces as a generalization of the almost-Lindelöf spaces and as a new and significative application of the quasi-regular open subsets of [1].

Keywords

• Lindelöf space
• almost Lindelöf
• weakly Lindelöf and nearly Lindelöf
• semiregular and almost-regular space
• regular cover.