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Weaker Forms of Soft Regular and Soft T 2 Soft Topological Spaces

Author

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  • Samer Al Ghour

    (Department of Mathematics, Jordan University of Science and Technology, Irbid 22110, Jordan)

Abstract

Soft ω -local indiscreetness as a weaker form of both soft local countability and soft local indiscreetness is introduced. Then soft ω -regularity as a weaker form of both soft regularity and soft ω -local indiscreetness is defined and investigated. Additionally, soft ω - T 2 as a new soft topological property that lies strictly between soft T 2 and soft T 1 is defined and investigated. It is proved that soft anti-local countability is a sufficient condition for equivalence between soft ω -locally indiscreetness (resp. soft ω -regularity) and soft locally indiscreetness (resp. soft ω -regularity). Additionally, it is proved that the induced topological spaces of a soft ω -locally indiscrete (resp. soft ω -regular, soft ω - T 2 ) soft topological space are (resp. ω -regular, ω - T 2 ) topological spaces. Additionally, it is proved that the generated soft topological space of a family of ω -locally indiscrete (resp. ω -regular, ω - T 2 ) topological spaces is soft ω -locally indiscrete and vice versa. In addition to these, soft product theorems regarding soft ω -regular and soft ω - T 2 soft topological spaces are obtained. Moreover, it is proved that soft ω -regular and soft ω - T 2 are hereditarily under soft subspaces.

Suggested Citation

  • Samer Al Ghour, 2021. "Weaker Forms of Soft Regular and Soft T 2 Soft Topological Spaces," Mathematics, MDPI, vol. 9(17), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2153-:d:628648
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    References listed on IDEAS

    as
    1. Tareq M. Al-shami & Ahmed Mostafa Khalil, 2021. "Bipolar Soft Sets: Relations between Them and Ordinary Points and Their Applications," Complexity, Hindawi, vol. 2021, pages 1-14, January.
    2. 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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    Citations

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    Cited by:

    1. Samer Al Ghour, 2022. "Between the Classes of Soft Open Sets and Soft Omega Open Sets," Mathematics, MDPI, vol. 10(5), pages 1-14, February.
    2. Samer Al Ghour & Hanan Al-Saadi, 2023. "Soft ω - θ -Continuous and Soft Weakly θ ω -Continuous Mappings," Mathematics, MDPI, vol. 11(19), pages 1-15, September.

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