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18 pages, 358 KiB

Open AccessArticle

Two New Families of Supra-Soft Topological Spaces Defined by Separation Axioms

by Tareq M. Al-shami, José Carlos R. Alcantud and A. A. Azzam

Mathematics 2022, 10(23), 4488; https://doi.org/10.3390/math10234488 - 28 Nov 2022

Cited by 17 | Viewed by 1766

This paper contributes to the field of supra-soft topology. We introduce and investigate supra

p p

-soft

T_{j}

and supra

p t

-soft

T_{j}

-spaces

(j = 0, 1, 2, 3, 4)

. These are [...] Read more.

This paper contributes to the field of supra-soft topology. We introduce and investigate supra

p p

-soft

T_{j}

and supra

p t

-soft

T_{j}

-spaces

(j = 0, 1, 2, 3, 4)

. These are defined in terms of different ordinary points; they rely on partial belong and partial non-belong relations in the first type, and partial belong and total non-belong relations in the second type. With the assistance of examples, we reveal the relationships among them as well as their relationships with classes of supra-soft topological spaces such as supra

t p

-soft

T_{j}

and supra

t t

-soft

T_{j}

-spaces

(j = 0, 1, 2, 3, 4)

. This work also investigates both the connections among these spaces and their relationships with the supra topological spaces that they induce. Some connections are shown with the aid of examples. In this regard, we prove that for

i = 0, 1

, possessing the

T_{i}

property by a parametric supra-topological space implies possessing the

p p

-soft

T_{i}

property by its supra-soft topological space. This relationship is invalid for the other types of soft spaces introduced in previous literature. We derive some results of

p p

-soft

T_{i}

-spaces from the cardinality numbers of the universal set and a set of parameters. We also demonstrate how these spaces behave as compared to their counterparts studied in soft topology and its generalizations (such as infra-soft topologies and weak soft topologies). Moreover, we investigated whether subspaces, finite product spaces, and soft

S^{Full article(This article belongs to the Section D2: Operations Research and Fuzzy Decision Making)13 pages,                803 KiB Open Access Article Connectedness and Local Connectedness on Infra Soft Topological Spaces by Tareq M. Al-shami and El-Sayed A. Abo-Tabl Mathematics 2021, 9 (15), 1759; https://doi.org/10.3390/math9151759 - 26 Jul 2021 Cited by 23 | Viewed by 2684 Abstract This year, we introduced the concept of infra soft topology as a new generalization of soft topology. To complete our analysis of this space, we devote this paper to presenting the concepts of infra soft connected and infra soft locally connected spaces. We [...] Read more. This year, we introduced the concept of infra soft topology as a new generalization of soft topology. To complete our analysis of this space, we devote this paper to presenting the concepts of infra soft connected and infra soft locally connected spaces. We provide some descriptions for infra soft connectedness and elucidate that there is no relationship between an infra soft topological space and its parametric infra topological spaces with respect to the property of infra soft connectedness. We discuss the behaviors of infra soft connected and infra soft locally connected spaces under infra soft homeomorphism maps and a finite product of soft spaces. We complete this manuscript by defining a component of a soft point and establishing its main properties. We determine the conditions under which the number of components is finite or countable, and we discuss under what conditions the infra soft connected subsets are components. 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                    $('#refineYearRange').click(function () {
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            setTimeout(function(){
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        });}

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