Soft ω*-Paracompactness in Soft Topological Spaces

Ghour, Samer Al

doi:10.5391/ijfis.2021.21.1.57

Cited by 13 publications

(10 citation statements)

References 9 publications

(16 reference statements)

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“…is concept was independently reformulated by Samanta et al [11,12], while Das and Samanta [11] applied the new version of the soft point to study the concept of soft metric spaces and Nazmul and Samanta [12] used it to discuss soft neighbourhood systems and reveal some relations of soft limit points of a soft set. Many scholars analyzed the properties of soft topologies and compared their performance with the case of classical topologies, see, for example, [13][14][15][16][17][18][19][20][21][22][23]. Generalizations of open sets were investigated in soft topologies, see [24,25].…”

Section: Introductionmentioning

confidence: 99%

New Soft Structure: Infra Soft Topological Spaces

Al-shami

2021

Mathematical Problems in Engineering

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It is always convenient to find the weakest conditions that preserve some topologically inspired properties. To this end, we introduce the concept of an infra soft topology which is a collection of subsets that extend the concept of soft topology by dispensing with the postulate that the collection is closed under arbitrary unions. We study the basic concepts of infra soft topological spaces such as infra soft open and infra soft closed sets, infra soft interior and infra soft closure operators, and infra soft limit and infra soft boundary points of a soft set. We reveal the main properties of these concepts with the help of some elucidative examples. Then, we present some methods to generate infra soft topologies such as infra soft neighbourhood systems, basis of infra soft topology, and infra soft relative topology. We also investigate how we initiate an infra soft topology from crisp infra topologies. In the end, we explore the concept of continuity between infra soft topological spaces and determine the conditions under which the continuity is preserved between infra soft topological space and its parametric infra topological spaces.

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Section: Introductionmentioning

confidence: 99%

New Soft Structure: Infra Soft Topological Spaces

Al-shami

2021

Mathematical Problems in Engineering

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“…The family of all soft closed sets in (X, τ, A) will be denoted by τ c . Soft topological concepts and their applications are still a hot area of research ( [1,2,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]). The notion of ω-regular TSs was introduced in [23], then the study of ω-regular TSs continued in [24] in which the authors defined and investigated ω-T 2 TSs.…”

Section: Introductionmentioning

confidence: 99%

Weaker Forms of Soft Regular and Soft T2 Soft Topological Spaces

Ghour

2021

Mathematics

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Soft ω-local indiscreetness as a weaker form of both soft local countability and soft local indiscreetness is introduced. Then soft ω-regularity as a weaker form of both soft regularity and soft ω-local indiscreetness is defined and investigated. Additionally, soft ω-T2 as a new soft topological property that lies strictly between soft T2 and soft T1 is defined and investigated. It is proved that soft anti-local countability is a sufficient condition for equivalence between soft ω-locally indiscreetness (resp. soft ω-regularity) and soft locally indiscreetness (resp. soft ω-regularity). Additionally, it is proved that the induced topological spaces of a soft ω-locally indiscrete (resp. soft ω-regular, soft ω-T2) soft topological space are (resp. ω-regular, ω-T2) topological spaces. Additionally, it is proved that the generated soft topological space of a family of ω-locally indiscrete (resp. ω-regular, ω-T2) topological spaces is soft ω-locally indiscrete and vice versa. In addition to these, soft product theorems regarding soft ω-regular and soft ω-T2 soft topological spaces are obtained. Moreover, it is proved that soft ω-regular and soft ω-T2 are hereditarily under soft subspaces.

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“…For a STS (U, τ, E), the members τ are called soft open sets. Soft topological concepts and their applications are still a hot area of research [1,2,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The concept of ω-open sets in TSs is defined in [23] as follows: let (U, ) be a TS and V ⊆ U, then V is ω-open set in (U, ) if for each x ∈ V, there is W ∈ such that x ∈ W and W − V is countable, or equivalently, V is ω-open set in (U, ) if and only if for each x ∈ V, there is W ∈ and a countable set C ⊆ U such that x ∈ W −C ⊆ V. Denote the family of all ω-open sets in the TS (U, ) by ω .…”

Section: Introductionmentioning

confidence: 99%

“…Three types of ω-open sets were defined and studied in bitopological spaces in [30]. Recently, soft ω-open sets were defined and investigated in STSs in [2], and research via them was continued in [5,31]. As a generalization of BTSs and as an extension of STSs, SBTSs were defined and investigated in [32].…”

Section: Introductionmentioning

confidence: 99%

Some Modifications of Pairwise Soft Sets and Some of Their Related Concepts

Ghour

2021

Mathematics

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In this paper, we first define soft u-open sets and soft s-open as two new classes of soft sets on soft bitopological spaces. We show that the class of soft p-open sets lies strictly between these classes, and we give several sufficient conditions for the equivalence between soft p-open sets and each of the soft u-open sets and soft s-open sets, respectively. In addition to these, we introduce the soft u-ω-open, soft p-ω-open, and soft s-ω-open sets as three new classes of soft sets in soft bitopological spaces, which contain soft u-open sets, soft p-open sets, and soft s-open sets, respectively. Via soft u-open sets, we define two notions of Lindelöfeness in SBTSs. We discuss the relationship between these two notions, and we characterize them via other types of soft sets. We define several types of soft local countability in soft bitopological spaces. We discuss relationships between them, and via some of them, we give two results related to the discrete soft topological space. According to our new concepts, the study deals with the correspondence between soft bitopological spaces and their generated bitopological spaces.

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Soft ω*-Paracompactness in Soft Topological Spaces

Cited by 13 publications

References 9 publications

New Soft Structure: Infra Soft Topological Spaces

New Soft Structure: Infra Soft Topological Spaces

Weaker Forms of Soft Regular and Soft T2 Soft Topological Spaces

Some Modifications of Pairwise Soft Sets and Some of Their Related Concepts

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