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Quaestiones Mathematicae

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A note on monotonically star Lindelöf spaces

Yan-Kui Song

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




http://dx.doi.org/10.2989/16073606.2017.1306004
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