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Soft super-continuity and soft delta-closed graphs

Author

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  • Dina Abuzaid
  • Samer Al Ghour
  • Monia Naghi

Abstract

Introducing a strong form of soft continuity between soft topological spaces is significant because it can contribute to our growing understanding of soft topological spaces and their features, provide a basis for creating new mathematical tools and methods, and have significant applications in various fields. In this paper, we define soft super-continuity as a new form of soft mapping. We present various characterizations of this soft concept. Also, we show that soft super-continuity lies strictly between soft continuity and soft complete continuity and that soft super-continuity is a strong form of soft δ-continuity. In addition, we give some sufficient conditions for the equivalence between soft super-continuity and other related concepts. Moreover, we characterize soft semi-regularity in terms of super-continuity. Furthermore, we provide several results of soft composition, restrictions, preservation, and products by soft super-continuity. In addition to these, we study the relationship between soft super-continuity and soft δ-continuity with their analogous notions in general topology. Finally, we give several sufficient conditions on a soft mapping to have a soft δ-closed graph.

Suggested Citation

  • Dina Abuzaid & Samer Al Ghour & Monia Naghi, 2024. "Soft super-continuity and soft delta-closed graphs," PLOS ONE, Public Library of Science, vol. 19(4), pages 1-18, April.
    • Handle: RePEc:plo:pone00:0301705
    DOI: 10.1371/journal.pone.0301705
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    References listed on IDEAS

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    1. Metin Akdag & Alkan Ozkan, 2014. "Soft -Open Sets and Soft -Continuous Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, February.
    2. Bin Chen, 2013. "Some Local Properties of Soft Semi-Open Sets," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-6, April.
    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. Metin Akdag & Alkan Ozkan, 2014. "Soft α‐Open Sets and Soft α‐Continuous Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
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