Nearly Soft Menger Spaces

Al-shami, Tareq M.; Kočinac, Ljubiša D.R.

doi:10.1155/2020/3807418

Cited by 27 publications

(15 citation statements)

References 30 publications

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“…e work of Shabir and Nazs [7], in particular, was crucial in establishing the field of soft topology. After that various classes of soft topological spaces have been proposed, such as: soft compact [8], soft connected [9], soft paracompact [9], soft extremely disconnected [10], and soft separable spaces [11], soft J-spaces [12], soft Menger spaces [13] and soft separation axioms [11,14]. At this point, it is worth remarking that not all classical results in topology are true in soft topology, see eorem 4 in [15].…”

Section: Introductionmentioning

confidence: 99%

Maximal Soft Compact and Maximal Soft Connected Topologies

Ghour

Ameen

2022

Applied Computational Intelligence and Soft Computing

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In various articles, it is said that the class of all soft topologies on a common universe forms a complete lattice, but in this paper, we prove that it is a complete lattice. Some soft topologies are maximal, and some are minimal with respect to specific soft topological properties. We study the properties of soft compact and soft connected topologies that are maximal. Particularly, we prove that a maximal soft compact topology has identical families of soft compact and soft closed sets. We further show that a maximal soft compact topology is soft T 1 , while a maximal soft connected topology is soft T 0 . Lastly, we establish that each soft connected relative topology to a maximal soft connected topology is maximal.

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Section: Introductionmentioning

confidence: 99%

Maximal Soft Compact and Maximal Soft Connected Topologies

Ghour

Ameen

2022

Applied Computational Intelligence and Soft Computing

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“…Shabir and Naz [11] initiated soft topology, which is a new branch of topology that combines soft set theory and topology. Since that time, the generalization of topological concepts in soft topology has become the focus of many researchers, such as soft compact [12], soft connected [13], soft paracompact [13], soft extremely disconnected [14], soft Menger spaces [15], soft separable spaces [16], soft separation axioms [17][18][19], soft metric spaces [20][21][22], soft homogeneous spaces [23,24], and soft maps [25,26], and substantial contributions can still be made.…”

Section: Introductionmentioning

confidence: 99%

Between the Classes of Soft Open Sets and Soft Omega Open Sets

Ghour

2022

Mathematics

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In this paper, we define the class of soft ω0-open sets. We show that this class forms a soft topology that is strictly between the classes of soft open sets and soft ω-open sets, and we provide some sufficient conditions for the equality of the three classes. In addition, we show that soft closed soft ω-open sets are soft ω0-open sets in soft Lindelof soft topological spaces. Moreover, we study the correspondence between soft ω0-open sets in soft topological spaces and ω0-open sets in topological spaces. Furthermore, we investigate the relationships between the soft α-open sets (respectively, soft regular open sets, soft β-open sets) of a given soft anti-locally countable soft topological space and the soft α-open sets (respectively, soft regular open sets, soft β-open sets) of the soft topological space of soft ω0-open sets generated by it. Finally, we introduce ω0-regularity in topological spaces via ω0-open sets, which is strictly between regularity and ω-regularity, and we also introduce soft ω0-regularity in soft topological spaces via soft ω0-open sets, which is strictly between soft regularity and soft ω-regularity. We investigate relationships regarding ω0-regularity and soft ω0-regularity. Moreover, we study the correspondence between soft ω0-regularity in soft topological spaces and ω0-regularity in topological spaces.

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“…Shabir and Naz's [30] contributions were especially important in establishing the area of soft topology. Later several subclasses of soft topological spaces were suggested, including soft separation axioms [1] , [3] , [14] , soft separable spaces [14] , soft connected [25] , soft compact [13] , [32] , soft paracompact [25] , soft extremally disconnected [11] , soft J-spaces [27] , and soft (nearly) Menger spaces [4] , [24] . Furthermore, soft bioperators on soft topological spaces have been studied in [12] .…”

Section: Introductionmentioning

confidence: 99%