More on μ-semi-Lindelöf sets in μ-spaces
Sarsak [On μ\mu -compact sets in μ\mu -spaces, Questions Answers Gen. Topology 31 (2013), no. 1, 49–57] introduced and studied the class of μ\mu -Lindelöf sets in μ\mu -spaces. Mustafa [μ\mu -semi compactness and μ\mu -semi Lindelöfness in generalized...
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| Formato: | article |
| Lenguaje: | EN |
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De Gruyter
2021
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| Acceso en línea: | https://doaj.org/article/6caf0d7cd498488390c95fb0a7734fe5 |
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| Sumario: | Sarsak [On
μ\mu -compact sets in
μ\mu -spaces, Questions Answers Gen. Topology 31 (2013), no. 1, 49–57] introduced and studied the class of μ\mu -Lindelöf sets in μ\mu -spaces. Mustafa [μ\mu -semi compactness and
μ\mu -semi Lindelöfness in generalized topological spaces, Int. J. Pure Appl. Math. 78 (2012), no. 4, 535–541] introduced and studied the class of μ\mu -semi-Lindelöf sets in generalized topological spaces (GTSs); the primary purpose of this paper is to investigate more properties and mapping properties of μ\mu -semi-Lindelöf sets in μ\mu -spaces. The class of μ\mu -semi-Lindelöf sets in μ\mu -spaces is a proper subclass of the class of μ\mu -Lindelöf sets in μ\mu -spaces. It is shown that the property of being μ\mu -semi-Lindelöf is not monotonic, that is, if (X,μ)\left(X,\mu ) is a μ\mu -space and A⊂B⊂XA\subset B\subset X, where AA is μB{\mu }_{B}-semi-Lindelöf, then AA need not be μ\mu -semi-Lindelöf. We also introduce and study a new type of generalized open sets in GTSs, called ωμ{\omega }_{\mu }-semi-open sets, and investigate them to obtain new properties and characterizations of μ\mu -semi-Lindelöf sets in μ\mu -spaces. |
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