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Article

Caliber and Chain Conditions in Soft Topologies

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BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, E37007 Salamanca, Spain
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Department of Mathematics, Sana’a University, Sana’a P.O. Box 1247, Yemen
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Department of Mathematics, Faculty of Science and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
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Department of Mathematics, Faculty of Science, New Valley University, Elkharga 72511, Egypt
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Author to whom correspondence should be addressed.
Academic Editor: Francisco Gallego Lupiaňez
Mathematics 2021, 9(19), 2349; https://doi.org/10.3390/math9192349
Received: 6 September 2021 / Revised: 18 September 2021 / Accepted: 18 September 2021 / Published: 22 September 2021
(This article belongs to the Special Issue Fuzzy Sets and Artificial Intelligence)
In this paper, we contribute to the growing literature on soft topology. Its theoretical underpinning merges point-set or classical topology with the characteristics of soft sets (a model for the representation of uncertain knowledge initiated in 1999). We introduce two types of axioms that generalize suitable concepts of soft separability. They are respectively concerned with calibers and chain conditions. We investigate explicit procedures for the construction of non-trivial soft topological spaces that satisfy these new axioms. Then we explore the role of cardinality in their study, and the relationships among these and other properties. Our results bring to light a fruitful field for future research in soft topology. View Full-Text
Keywords: soft topology; topology; countable chain condition; caliber; separability soft topology; topology; countable chain condition; caliber; separability
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MDPI and ACS Style

Alcantud, J.C.R.; Al-shami, T.M.; Azzam, A.A. Caliber and Chain Conditions in Soft Topologies. Mathematics 2021, 9, 2349. https://doi.org/10.3390/math9192349

AMA Style

Alcantud JCR, Al-shami TM, Azzam AA. Caliber and Chain Conditions in Soft Topologies. Mathematics. 2021; 9(19):2349. https://doi.org/10.3390/math9192349

Chicago/Turabian Style

Alcantud, José C.R., Tareq M. Al-shami, and A. A. Azzam. 2021. "Caliber and Chain Conditions in Soft Topologies" Mathematics 9, no. 19: 2349. https://doi.org/10.3390/math9192349

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