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

• Autorzy: Sarsak Mohammad S.

Identyfikatory

DOI

10.1515/dema-2021-0026

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

generalized topology; μ-space; μ-open; μ-semi-open; μ-Lindelöf set; μ-Lindelöf space; μ-semi-Lindelöf set; μ-semi-Lindelöf space

PL

topologia ogólna; przestrzeń; zbiór; μ-otwarty; μ-półotwarty; przestrzeń Lindelofa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2021
• Tom: Vol. 54, nr 1
• Strony: 259--271
• Opis fizyczny: Bibliogr. 36 poz.

Twórcy

autor

Sarsak Mohammad S.

• Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan

Bibliografia

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Uwagi

PL

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