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More properties of generalized open sets in generalized topological spaces

Sarsak Mohammad S.

Demonstratio Mathematica

2022

Vol. 55, nr 1

404--415

Sarsak [M. S. Sarsak, On some properties of generalized open sets in generalized topological spaces, Demonstr. Math. 46 (2013), no. 2, 415–427] studied some properties of generalized open sets in generalized topological spaces (GTSs); the primary purpose of this article is to investigate more properties of generalized open sets in GTSs. We mainly study the behaviours of regular closed sets, semi-open sets, regular semi-open sets, preopen sets, and β -open sets in GTSs analogous to their behaviours in topological spaces.

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

Sarsak Mohammad S.

Demonstratio Mathematica

2021

Vol. 54, nr 1

259--271

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.