Soft maps via soft somewhere dense sets

Al-shami, Tareq M.; Alshammari, Ibtesam; Asaad, Baravan A.

doi:10.2298/fil2010429a

Cited by 38 publications

(24 citation statements)

References 20 publications

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“…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]. In [26], we corrected some alleged results concerning soft separation axioms, especially those defined using soft points.…”

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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“…Shabir and Naz [45] initiated the idea of soft topological spaces and studied soft separation axioms. Later on, many researchers carried out several studies to discuss the topological notions on soft topologies (see, for example [2,3,7,11,15,20,22,29,30,31,36,44]). Chen [24] and Mahanta and Das [37] displayed and probed the notions of soft semi open sets and soft semi separation axioms.…”

Section: Introductionmentioning

confidence: 99%

Defining and investigating new soft ordered maps by using soft semi open sets

Al-shami

2021

Acta Universitatis Sapientiae, Mathematica

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Here, we employ soft semi open sets to define new soft ordered maps, namely soft x-semi continuous, soft x-semi open, soft x-semi closed and soft x-semi homeomorphism maps, where x denotes the type of monotonicity. To show the relationships among them, we provide some illustrative examples. Then we give complete descriptions for each one of them. Also, we investigate “transmission” of these maps between soft and classical topological ordered spaces.

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Soft maps via soft somewhere dense sets

Cited by 38 publications

References 20 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

Defining and investigating new soft ordered maps by using soft semi open sets

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