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Soft Semi ω -Open Sets

Author

Listed:
  • Samer Al Ghour

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

Abstract

In this paper, we introduce the class of soft semi ω -open sets of a soft topological space ( X , τ , A ) , using soft ω -open sets. We show that the class of soft semi ω -open sets contains both the soft topology τ ω and the class of soft semi-open sets. Additionally, we define soft semi ω -closed sets as the class of soft complements of soft semi ω -open sets. We present here a study of the properties of soft semi ω -open sets, especially in ( X , τ , A ) and ( X , τ ω , A ) . In particular, we prove that the class of soft semi ω -open sets is closed under arbitrary soft union but not closed under finite soft intersections; we also study the correspondence between the soft topology of soft semi ω -open sets of a soft topological space and their generated topological spaces and vice versa. In addition to these, we introduce the soft semi ω -interior and soft semi ω -closure operators via soft semi ω -open and soft semi ω -closed sets. We prove several equations regarding these two new soft operators. In particular, we prove that these operators can be calculated using other usual soft operators in both of ( X , τ , A ) and ( X , τ ω , A ) , and some equations focus on soft anti-locally countable soft topological spaces.

Suggested Citation

  • Samer Al Ghour, 2021. "Soft Semi ω -Open Sets," Mathematics, MDPI, vol. 9(24), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3168-:d:698233
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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.
    3. T. M. Al-shami & Ching-Feng Wen, 2021. "Compactness on Soft Topological Ordered Spaces and Its Application on the Information System," Journal of Mathematics, Hindawi, vol. 2021, pages 1-12, January.
    4. Sagvan Y. Musa & Baravan A. Asaad, 2021. "Bipolar Hypersoft Sets," Mathematics, MDPI, vol. 9(15), pages 1-15, August.
    Full references (including those not matched with items on IDEAS)

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