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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oai:doaj.org-article:6caf0d7cd498488390c95fb0a7734fe52021-12-05T14:10:45ZMore on μ-semi-Lindelöf sets in μ-spaces2391-466110.1515/dema-2021-0026https://doaj.org/article/6caf0d7cd498488390c95fb0a7734fe52021-08-01T00:00:00Zhttps://doi.org/10.1515/dema-2021-0026https://doaj.org/toc/2391-4661Sarsak [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.Sarsak Mohammad S.De Gruyterarticlegeneralized topologyμ-spaceμ-openμ-semi-openμ-lindelöf setμ-lindelöf spaceμ-semi-lindelöf setμ-semi-lindelöf space54a0554a1054d20MathematicsQA1-939ENDemonstratio Mathematica, Vol 54, Iss 1, Pp 259-271 (2021) |
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generalized topology μ-space μ-open μ-semi-open μ-lindelöf set μ-lindelöf space μ-semi-lindelöf set μ-semi-lindelöf space 54a05 54a10 54d20 Mathematics QA1-939 |
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generalized topology μ-space μ-open μ-semi-open μ-lindelöf set μ-lindelöf space μ-semi-lindelöf set μ-semi-lindelöf space 54a05 54a10 54d20 Mathematics QA1-939 Sarsak Mohammad S. More on μ-semi-Lindelöf sets in μ-spaces |
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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. |
| format |
article |
| author |
Sarsak Mohammad S. |
| author_facet |
Sarsak Mohammad S. |
| author_sort |
Sarsak Mohammad S. |
| title |
More on μ-semi-Lindelöf sets in μ-spaces |
| title_short |
More on μ-semi-Lindelöf sets in μ-spaces |
| title_full |
More on μ-semi-Lindelöf sets in μ-spaces |
| title_fullStr |
More on μ-semi-Lindelöf sets in μ-spaces |
| title_full_unstemmed |
More on μ-semi-Lindelöf sets in μ-spaces |
| title_sort |
more on μ-semi-lindelöf sets in μ-spaces |
| publisher |
De Gruyter |
| publishDate |
2021 |
| url |
https://doaj.org/article/6caf0d7cd498488390c95fb0a7734fe5 |
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AT sarsakmohammads moreonmsemilindelofsetsinmspaces |
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