On Soft<i>β</i>-Open Sets and Soft<i>β</i>-Continuous Functions

Akdağ, Metin; Özkan, Alkan

doi:10.1155/2014/843456

Cited by 30 publications

(16 citation statements)

References 9 publications

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“…The set of all soft points in SS(Y, B) will be denoted SP(X, A). [28] (respectively, soft β-open [29], soft regular open [31] Theorem 2. Ref.…”

Section: Preliminariesmentioning

confidence: 99%

“…Generalizations of soft open sets play an effective role in soft topology through their use to improve on some known results or to open the door to redefine and investigate some of the soft topological concepts such as soft compactness, soft correlation, soft class axioms, soft assignments, etc. Some important generalizations of soft open sets appear in [27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

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Between the Classes of Soft Open Sets and Soft Omega Open Sets

Ghour

2022

Mathematics

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In this paper, we define the class of soft ω0-open sets. We show that this class forms a soft topology that is strictly between the classes of soft open sets and soft ω-open sets, and we provide some sufficient conditions for the equality of the three classes. In addition, we show that soft closed soft ω-open sets are soft ω0-open sets in soft Lindelof soft topological spaces. Moreover, we study the correspondence between soft ω0-open sets in soft topological spaces and ω0-open sets in topological spaces. Furthermore, we investigate the relationships between the soft α-open sets (respectively, soft regular open sets, soft β-open sets) of a given soft anti-locally countable soft topological space and the soft α-open sets (respectively, soft regular open sets, soft β-open sets) of the soft topological space of soft ω0-open sets generated by it. Finally, we introduce ω0-regularity in topological spaces via ω0-open sets, which is strictly between regularity and ω-regularity, and we also introduce soft ω0-regularity in soft topological spaces via soft ω0-open sets, which is strictly between soft regularity and soft ω-regularity. We investigate relationships regarding ω0-regularity and soft ω0-regularity. Moreover, we study the correspondence between soft ω0-regularity in soft topological spaces and ω0-regularity in topological spaces.

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“…The set of all soft points in SS(Y, B) will be denoted SP(X, A). [28] (respectively, soft β-open [29], soft regular open [31] Theorem 2. Ref.…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Between the Classes of Soft Open Sets and Soft Omega Open Sets

Ghour

2022

Mathematics

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“…B. Chen [3] studied soft semi-open sets & associated concepts on STSs. Metin Akdag et al [8,9] elucidated "soft 𝛼-open (closed) sets, soft -open (closed) sets, soft α-continuous fu n ct i o n s and soft -continuous f un ct i o ns ". And they studied interrelation of soft continuity, soft semi continuity, soft 𝛼-continuity and soft -continuity of mappings described on STS.…”

mentioning

confidence: 99%

Exploring Quantum and Binary Soft í µí»¼–Open Sets:Practical Applications through Soft Topologies

2024

Preprint

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This paper presents an exploration of Quantum and Binary Soft 𝛼 –Open Sets, focusing on their practical applications within the framework of soft topologies. In the binary soft topological spaces, binary soft 𝛼-closures, binary soft 𝛼-interiors and binary soft 𝛼-open (closed) sets are defined and study many of their properties along with how these concepts are connected to other soft open (closed) sets via theorems and propositions. The non-coincidence of these soft set theory concepts are proven via the use of counter examples. Further we look into the idea of binary soft 𝛼-continuous function which is described on family of binary soft 𝛼-open (closed) sets referred to as soft class over two starting universes with parameters, as well as their links to other soft continuous and weaker sections of soft continuous functions. The findings of this study represent the beginning of a new soft structure that will work as theoretical base for topological applications on soft sets, and will also act as a springboard for the extension of information systems and other engineering disciplines. Additionally, we demonstrate how binary soft set concept can be applied in medical information system. AMS Subject Classifications: 54A05, 54C08, 54A99

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“…This conclusion is not correct since

false(F_{normal2}, E false) \overset{\cap}{true} false(F_{normal7}, E false) \notin τ

false(F_{normal3}, E false) \overset{\cup}{true} false(F_{normal8}, E false) \notin τ

false(F_{normal1}, E false) \overset{\cup}{true} false(F_{normal13}, E false) \notin τ

false(F_{normal1}, E false) \overset{\cap}{true} false(F_{normal13}, E false) \notin τ

false(F_{normal2}, E false) \overset{\cap}{true} false(F_{normal13}, E false) \overset{\cap}{true} false(F_{normal13}, E false) \notin τ

false(F_{normal2}, E false) \overset{\cup}{true} false(F_{normal13}, E false) \notin τ

false(F_{normal2}, E false) \overset{\cap}{true} false(F_{normal14}, E false) \notin τ

, and many of soft sets belong to the family τ and their soft intersection and soft union do not exist in τ . Consequently, [1, Examples 27, 28, 29, 30] also are incorrect. Example 3.3 in [2] already proved the results in [1, Remark 12] and [2, Examples 4.3 and 4.4] also proved the results in [1, Remark 26].…”

mentioning

confidence: 99%

“…Consequently, [1, Examples 27, 28, 29, 30] also are incorrect. Example 3.3 in [2] already proved the results in [1, Remark 12] and [2, Examples 4.3 and 4.4] also proved the results in [1, Remark 26].…”

mentioning

confidence: 99%