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Soft Separation Axioms and Fixed Soft Points Using Soft Semiopen Sets

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  • T. M. Al-shami

Abstract

The importance of soft separation axioms comes from their vital role in classifications of soft spaces, and their interesting properties are studied. This article is devoted to introducing the concepts of tt‐soft semi‐Ti(i = 0, 1, 2, 3, 4) and tt‐soft semiregular spaces with respect to ordinary points. We formulate them by utilizing the relations of total belong and total nonbelong. The advantages behind using these relations are, first, generalization of existing comparable properties on general topology and, second, eliminating the stability shape of soft open and closed subsets of soft semiregular spaces. By some examples, we show the relationships between them as well as with soft semi‐Ti(i = 0, 1, 2, 3, 4) and soft semiregular spaces. Also, we explore under what conditions they are kept between soft topology and its parametric topologies. We characterize a tt‐soft semiregular space and demonstrate that it guarantees the equivalence of tt‐soft semi‐Ti(i = 0, 1, 2). Further, we investigate some interrelations of them and some soft topological notions such as soft compactness, product soft spaces, and sum of soft topological spaces. Finally, we define a concept of semifixed soft point and study its main properties.

Suggested Citation

  • T. M. Al-shami, 2020. "Soft Separation Axioms and Fixed Soft Points Using Soft Semiopen Sets," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnljam:v:2020:y:2020:i:1:n:1746103
    DOI: 10.1155/2020/1746103
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    References listed on IDEAS

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    1. José Carlos R. Alcantud, 2020. "Soft Open Bases and a Novel Construction of Soft Topologies from Bases for Topologies," Mathematics, MDPI, vol. 8(5), pages 1-12, April.
    2. Tareq M. Al-shami & LjubiÅ¡a D. R. KoÄ inac & Ali Jaballah, 2020. "Nearly Soft Menger Spaces," Journal of Mathematics, Hindawi, vol. 2020, pages 1-9, May.
    3. 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.
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    Cited by:

    1. Sagvan Y. Musa & Baravan A. Asaad, 2022. "Topological Structures via Bipolar Hypersoft Sets," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).

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