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Sum of Soft Topological Spaces

Author

Listed:
  • Tareq M. Al-shami

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

  • Ljubiša D. R. Kočinac

    (Faculty of Sciences and Mathematics, University of Niš, 18000 Niš, Serbia)

  • Baravan A. Asaad

    (Department of Computer Science, College of Science, Cihan University-Duhok, Duhok 42001, Iraq
    Department of Mathematics, Faculty of Science, University of Zakho, Zakho 42002, Iraq)

Abstract

In this paper, we introduce the concept of sum of soft topological spaces using pairwise disjoint soft topological spaces and study its basic properties. Then, we define additive and finitely additive properties which are considered a link between soft topological spaces and their sum. In this regard, we show that the properties of being p-soft T i , soft paracompactness, soft extremally disconnectedness, and soft continuity are additive. We provide some examples to elucidate that soft compactness and soft separability are finitely additive; however, soft hyperconnected, soft indiscrete, and door soft spaces are not finitely additive. In addition, we prove that soft interior, soft closure, soft limit, and soft boundary points are interchangeable between soft topological spaces and their sum. This helps to obtain some results related to some important generalized soft open sets. Finally, we observe under which conditions a soft topological space represents the sum of some soft topological spaces.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:990-:d:372620
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    References listed on IDEAS

    as
    1. 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.
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    Cited by:

    1. Samer Al Ghour, 2021. "Some Modifications of Pairwise Soft Sets and Some of Their Related Concepts," Mathematics, MDPI, vol. 9(15), pages 1-14, July.
    2. Samer Al Ghour, 2021. "Soft Semi ω -Open Sets," Mathematics, MDPI, vol. 9(24), pages 1-12, December.
    3. Nagarajan Kalaivani & Khaleel Fayaz Ur Rahman & Lenka Čepová & Robert Čep, 2022. "On Grill S β -Open Set in Grill Topological Spaces," Mathematics, MDPI, vol. 10(23), pages 1-9, December.
    4. Sagvan Y. Musa & Baravan A. Asaad, 2021. "Bipolar Hypersoft Sets," Mathematics, MDPI, vol. 9(15), pages 1-15, August.
    5. 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.
    6. 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.
    7. Tatiana Pedraza & Jesús Rodríguez-López, 2020. "Aggregation of L -Probabilistic Quasi-Uniformities," Mathematics, MDPI, vol. 8(11), pages 1-21, November.

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