On soft submaximal spaces

Ghour, Samer Al; Zanyar, A. Ameen

doi:10.1016/j.heliyon.2022.e10574

Cited by 9 publications

(6 citation statements)

References 25 publications

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“…More details about soft set theory and its applications in various mathematical structures may be found in [8,31,32]. Definition 5 ([12]).…”

Section: Definition 2 ([10]) Assumementioning

confidence: 99%

“…Molodtsov effectively utilized the soft set theory in [1,2] in several domains, including probability, measurement theory, Riemann integration, game theory, operation research, and smoothness of functions. Considerable advancements in theory and technology have resulted from an exponential growth in the study of and applications of this soft set (see [3][4][5][6][7][8][9]). Next, a well-focused investigation of an abstract soft set operator theory with applications to decision-making problems was conducted by Maji et al [10].…”

Section: Introductionmentioning

confidence: 99%

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Connectedness of Soft-Ideal Topological Spaces

Al-Omari,

Alqurashi

2024

Symmetry

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Despite its apparent simplicity, the idea of connectedness has significant effects on topology and its applications. An essential part of the intermediate-value theorem is the idea of connectedness. In many applications, such as population modeling, robotics motion planning, and geographic information systems, connectedness is significant, and it is a critical factor in differentiating between various topological spaces. This study uses soft open sets and the concept of soft ideals as a new class of soft sets to present and explore the ideas of soft connected spaces and strongly soft connected spaces with soft ideals. Also, under certain assumptions regarding the subsequent concepts—soft-ideal connectedness and stronglysoft-ideal connectedness in soft-ideal topological spaces—we characterize this new class of sets by employing soft open sets and soft ideals to examine its fundamental features. Furthermore, we look at a symmetry between our new notions and other existing ones, and this study examines the relationships between these concepts.

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“…More details about soft set theory and its applications in various mathematical structures may be found in [8,31,32]. Definition 5 ([12]).…”

Section: Definition 2 ([10]) Assumementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Connectedness of Soft-Ideal Topological Spaces

Al-Omari,

Alqurashi

2024

Symmetry

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“…After that, in soft set contexts, many traditional topological properties have been generalized, for instance, soft separation axioms [12], soft second countable spaces [13], soft separable spaces [12], soft connected spaces [14], soft compact spaces [15], soft extremally disconnected spaces [16], soft submaximal spaces [17], and soft paracompact spaces [14].…”

Section: Introductionmentioning

confidence: 99%

Some Classes of Soft Functions Defined by Soft Open Sets Modulo Soft Sets of the First Category

Ameen,

Alqahtani

2023

Mathematics

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Soft continuity can contribute to the development of digital images and computational topological applications other than the field of soft topology. In this work, we study a new class of generalized soft continuous functions defined on the class of soft open sets modulo soft sets of the first category, which is called soft functions with the Baire property. This class includes all soft continuous functions. More precisely, it contains various classes of weak soft continuous functions. The essential properties and operations of the soft functions with the Baire property are established. It is shown that a soft continuous with values in a soft second countable space is identical to a soft function with the Baire property, apart from a topologically negligible soft set. Then we introduce two more subclasses of soft functions with the Baire property and examine their basic properties. Furthermore, we characterize these subclasses in terms of soft continuous functions. At last, we present a diagram that shows the relationships between the classes of soft functions defined in this work and those that exist in the literature.

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“…Similarly, the notion of soft topology through soft grills was introduced in [13]. Additionally, a large number of academics and researchers developed gentle versions of the traditional topological ideas, such as soft resolvable spaces [14], soft hyperconnected spaces [15], suitable soft spaces [7], soft ideal spaces [4,16,17], soft extremally disconnected spaces [18], soft Menger spaces [19], soft countable chain condition, and soft caliber [20]. From here on, we shall refer to a soft ideal topological space (X E , τ, I), a soft ideal space.…”

Section: Introductionmentioning

confidence: 99%

“…For more details of soft set theory and its applications in a variety of mathematical structures, see [18,[23][24][25][26][27].…”

mentioning

confidence: 99%

Hyperconnectedness and Resolvability of Soft Ideal Topological Spaces

Al-Omari,

Alqurashi

2023

Mathematics

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This paper introduces and explores the concept of soft ideal dense sets, utilizing soft open sets and soft local functions, to examine their fundamental characteristics under some conditions for the following notions: soft ideal hyperconnectedness, soft ideal resolvability, soft ideal irresolvability, and soft ideal semi-irresolvability in soft ideal topological spaces. Moreover, it explores the relationship between these notions if τ⊓I¯=ϕE is obtained in the soft set environment.

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On soft submaximal spaces

Cited by 9 publications

References 25 publications

Connectedness of Soft-Ideal Topological Spaces

Connectedness of Soft-Ideal Topological Spaces

Some Classes of Soft Functions Defined by Soft Open Sets Modulo Soft Sets of the First Category

Hyperconnectedness and Resolvability of Soft Ideal Topological Spaces

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