A note on monotonically star Lindelöf spaces

Abstract

A space X is monotonically star Lindelöf if one assign to for each open cover U a subspace s(U) ⊆ X, called a kernel, such that s(U) is a Lindelöf subset of X, and st(s(U); U) = X, and if V renes U then ∪ s(U) ⊆ s(V), where st(s(U); U) = ∪ {U ∈ U : U ∩ s(U) ≠ ∅}. In this paper, we investigate the relationship between monotonically star Lindelöf spaces and related spaces, and also study topological properties of monotonically star Lindelöf spaces.

Keywords: Star covering properties, star Lindelöf, monotonically star Lindelöf