On soft parametric somewhat-open sets and applications via soft topologies

Al-shami, Tareq M.; Mhemdi, Abdelwaheb

doi:10.1016/j.heliyon.2023.e21472

Cited by 6 publications

(3 citation statements)

References 45 publications

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“…Therefore, this research area was and still is attractive to researchers. For instance, “soft semi-open” [ 24 ], “soft pre-open” [ 25 ], “soft β -open” [ 25 ], “soft θ -open” [ 26 ], “soft α -open” [ 27 ], “soft regular open” [ 28 ], “soft somewhere dense” [ 29 ], “soft δ -open” [ 30 ], “soft ω -open” [ 31 ], “weakly soft -open” [ 32 ], “soft γ -open” [ 33 ], “cluster soft sets” [ 34 ], “weakly soft β -open” [ 35 ], “weakly soft pre-open” [ 36 ], “soft parametric somewhat-open” [ 37 ], “weakly soft α -open” [ 38 ], and so on.…”

Section: Introductionmentioning

confidence: 99%

Soft super-continuity and soft delta-closed graphs

Abuzaid,

Al Ghour,

Naghi

2024

PLoS ONE

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Introducing a strong form of soft continuity between soft topological spaces is significant because it can contribute to our growing understanding of soft topological spaces and their features, provide a basis for creating new mathematical tools and methods, and have significant applications in various fields. In this paper, we define soft super-continuity as a new form of soft mapping. We present various characterizations of this soft concept. Also, we show that soft super-continuity lies strictly between soft continuity and soft complete continuity and that soft super-continuity is a strong form of soft δ-continuity. In addition, we give some sufficient conditions for the equivalence between soft super-continuity and other related concepts. Moreover, we characterize soft semi-regularity in terms of super-continuity. Furthermore, we provide several results of soft composition, restrictions, preservation, and products by soft super-continuity. In addition to these, we study the relationship between soft super-continuity and soft δ-continuity with their analogous notions in general topology. Finally, we give several sufficient conditions on a soft mapping to have a soft δ-closed graph.

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Section: Introductionmentioning

confidence: 99%

Soft super-continuity and soft delta-closed graphs

Abuzaid,

Al Ghour,

Naghi

2024

PLoS ONE

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“…Shabir and Naz [17] created soft topology first, and since then, a lot of researchers have focused on extending the topological concepts to include the field of soft topology. For instance, soft metric spaces [18][19][20], soft connected spaces [21], soft covering properties [22][23][24], and generalized soft open sets [25][26][27][28][29] are a few of the notions mentioned.…”

Section: Introduction and Preleminariesmentioning

confidence: 99%

On Soft ωδ-Open Sets and Some Decomposition Theorems

Abuzaid,

Al-Ghour,

Naghi

2024

Mathematics

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In this paper, we present a novel family of soft sets named “soft ωδ-open sets”. We find that this class constitutes a soft topology that lies strictly between the soft topologies of soft δ-open sets and soft ω0-open sets. Also, we introduce certain sufficient conditions for the equivalence between this new soft topology and several existing soft topologies. Moreover, we verify several relationships that contain soft covering properties, such as soft compactness and soft Lindelofness, which are related to this new soft topology. Furthermore, in terms of the soft interior operator in certain soft topologies, we define four classes of soft sets. Via them, we obtain new decomposition theorems for soft δ-openness and soft θ-openness, and we characterize the soft topological spaces that have the soft “semi-regularization property”. In addition, via soft ωδ-open sets, we introduce and investigate a new class of soft functions named “soft ωδ-continuous functions”. Finally, we look into the connections between the newly proposed soft concepts and their counterparts in classical topological spaces.

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“…Shabir and Naz demonstrated that soft topological notions are similar to those in classical topology, inspiring more study in this area. Since the inception of soft topology, there have been several contributions to the study of topological ideas in soft settings ( [14][15][16][17][18][19] are some of the recent). Majumdar and Samanta [20] discussed mappings on soft sets and their use in medical diagnostics.…”

Section: Introductionmentioning

confidence: 99%

Soft Faint Continuity and Soft Faint Theta Omega Continuity between Soft Topological Spaces

Abuzaid,

Naghi,

Al Ghour

2024

Symmetry

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The concepts of soft faint continuity as a weaker form of soft weak continuity and soft faint θω-continuity as a weaker form of soft weak θω-continuity are introduced. Numerous characterizations of them are given. We further demonstrate that, under soft restrictions, they are retained. Moreover, we show that a soft function is soft faintly continuous (respectively, soft faintly θω-continuous) if its soft graph function is soft faintly continuous (respectively, soft faintly θω-continuous). In addition, we show that a soft function with a soft almost regular (respectively, soft extremally disconnected) co-domain is soft faintly continuous iff it is soft almost continuous (respectively, soft δ-continuous). Furthermore, we show that soft faintly continuous surjective functions are soft set-connected functions, and as a corollary, we demonstrate how soft faintly continuous functions sustain soft connectivity. Finally, we studied the symmetry between our new notions and their topological counterparts.

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On soft parametric somewhat-open sets and applications via soft topologies

Cited by 6 publications

References 45 publications

Soft super-continuity and soft delta-closed graphs

Soft super-continuity and soft delta-closed graphs

On Soft ωδ-Open Sets and Some Decomposition Theorems

Soft Faint Continuity and Soft Faint Theta Omega Continuity between Soft Topological Spaces

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