Nearly Soft Î² - Open Sets via Soft Ditopological Spaces

Abu-Gdairi, Radwan Ahmad; Azzam, Abdelfattah; Noaman, Ibrahim

doi:10.29020/nybg.ejpam.v15i1.4249

Cited by 2 publications

(1 citation statement)

References 12 publications

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“…In [1,2] the concept based on Grl had been a useful tool like nets and filters for getting rooted deviation in further studying some topological properties like compactifications, along with extension problems of different kinds. Many more analyses, such as Al Hawary et al [3][4][5][6][7], had characterized and entrenched the properties based on Gene OS in the classical topo.…”

Section: Introductionmentioning

confidence: 99%

On Grill Sβ-Open Set in Grill Topological Spaces

et al. 2022

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In this article we originate a new class of Grill Set, namely GSβ-Open Set, which is parallel to the β Open Set in Grill Topological Space (X, θ, G). In addition, we entitle GSβ-continuous and GSβ-open functions by applying a GSβ-Open Set and we review some of its important properties. Many examples are given to explain the concept lucidly. The properties of GSβ open sets are investigated and studied. The theorems based on the arbitrary union and finite intersections are discussed with counter examples. Moreover, some operators like GSβ−closure and GSβ−interior are introduced and investigated. The concept of GSβ−continuous functions are compared with the idea of G−Semi Continuous function. The theorems based on GSβ−continunity have been proved.

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Section: Introductionmentioning

confidence: 99%

On Grill Sβ-Open Set in Grill Topological Spaces

et al. 2022

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New versions of maps and connected spaces via supra soft sd-operators

Abd El-latif,

Azzam,

Abu-Gdairi

et al. 2024

PLoS ONE

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In this manuscript we use novel types of soft operators to define new approaches of soft maps in the frame of supra soft topologies (or SSTSs), namely supra soft somewhere dens continuous (or SS-sd-continuous), SS-sd-open and SS-sd-closed maps. With the help of SS-closure (interior) operators and SS-sd-closure (interior) operators we succeed to introduce many equivalent conditions and several important properties to these notions. To name a few: We prove that there is an one to one between the SS-sd-open and SS-sd-closed maps under a bijective soft map, supported by counterexample to confirm the necessity of the bijectivity condition. Furthermore, we present the concept of SS-sd-separated sets with intersected characterizations, as a prelude to studying the connectedness in a supra soft topological space (or SSTS). Moreover, we show that, there is no priori relationship between supra soft-sd-connectedness in an SSTS and its parametric supra topological spaces in general, supported by concrete counterexamples. Finally, we prove that the image of an SS-sd-connected set under an SS-sd-irresolute map is an SS-sd-connected.

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Nearly Soft Î² - Open Sets via Soft Ditopological Spaces

Cited by 2 publications

References 12 publications

On Grill Sβ-Open Set in Grill Topological Spaces

On Grill Sβ-Open Set in Grill Topological Spaces

New versions of maps and connected spaces via supra soft sd-operators

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