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Some Classes of Soft Functions Defined by Soft Open Sets Modulo Soft Sets of the First Category

Author

Listed:
  • Zanyar A. Ameen

    (Department of Mathematics, College of Science, University of Duhok, Duhok 42001, Iraq)

  • Mesfer H. Alqahtani

    (Department of Mathematics, University College of Umluj, University of Tabuk, Tabuk 48322, Saudi Arabia)

Abstract

Soft continuity can contribute to the development of digital images and computational topological applications other than the field of soft topology. In this work, we study a new class of generalized soft continuous functions defined on the class of soft open sets modulo soft sets of the first category, which is called soft functions with the Baire property. This class includes all soft continuous functions. More precisely, it contains various classes of weak soft continuous functions. The essential properties and operations of the soft functions with the Baire property are established. It is shown that a soft continuous with values in a soft second countable space is identical to a soft function with the Baire property, apart from a topologically negligible soft set. Then we introduce two more subclasses of soft functions with the Baire property and examine their basic properties. Furthermore, we characterize these subclasses in terms of soft continuous functions. At last, we present a diagram that shows the relationships between the classes of soft functions defined in this work and those that exist in the literature.

Suggested Citation

  • Zanyar A. Ameen & Mesfer H. Alqahtani, 2023. "Some Classes of Soft Functions Defined by Soft Open Sets Modulo Soft Sets of the First Category," Mathematics, MDPI, vol. 11(20), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4368-:d:1264114
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    References listed on IDEAS

    as
    1. Zanyar A. Ameen & Tareq M. Al-shami & Radwan Abu-Gdairi & Abdelwaheb Mhemdi, 2023. "The Relationship between Ordinary and Soft Algebras with an Application," Mathematics, MDPI, vol. 11(9), pages 1-12, April.
    2. 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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