More on μ-semi-Lindelöf sets in μ-spaces

Sarsak [On μ-compact sets in μ-spaces, Questions Answers Gen. Topology 31 (2013), no. 1, 49-57] introduced and studied the class of μ-Lindelöf sets in μ-spaces. Mustafa [μ-semi compactness and μ-semi Lindelöfness in generalized topological spaces, Int. J. Pure Appl. Math. 78 (2012), no. 4, 535-541] introduced and studied the class of μ-semi-Lindelöf sets in generalized topological spaces (GTSs); the primary purpose of this paper is to investigate more properties and mapping properties of μ-semi-Lindelöf sets in μ-spaces. The class of μ-semi-Lindelöf sets in μ-spaces is a proper subclass of the class of μ-Lindelöf sets in μ-spaces. It is shown that the property of being μ-semi-Lindelöf is not monotonic, that is, if (X, μ) is a μ-space and A ⊂ B ⊂ X, where A is μB-semi-Lindelöf, then A need not be μ-semi-Lindelöf. We also introduce and study a new type of generalized open sets in GTSs, called ωμ-semi-open sets, and investigate them to obtain new properties and characterizations of μ-semi-Lindelöf sets in μ-spaces.

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Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).