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Caliber and Chain Conditions in Soft Topologies

Author

Listed:
  • José Carlos R. Alcantud

    (BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, E37007 Salamanca, Spain)

  • Tareq M. Al-shami

    (Department of Mathematics, Sana’a University, Sana’a P.O. Box 1247, Yemen)

  • A. A. Azzam

    (Department of Mathematics, Faculty of Science and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
    Department of Mathematics, Faculty of Science, New Valley University, Elkharga 72511, Egypt)

Abstract

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.

Suggested Citation

  • José Carlos R. Alcantud & Tareq M. Al-shami & A. A. Azzam, 2021. "Caliber and Chain Conditions in Soft Topologies," Mathematics, MDPI, vol. 9(19), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2349-:d:640299
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    References listed on IDEAS

    as
    1. Tareq M. Al-shami & Ljubiša D. R. Kočinac & Baravan A. Asaad, 2020. "Sum of Soft Topological Spaces," Mathematics, MDPI, vol. 8(6), pages 1-12, June.
    2. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
    3. Athar Kharal & B. Ahmad, 2011. "Mappings On Soft Classes," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 471-481.
    4. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
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