Soft super-continuity and soft delta-closed graphs

• Published in: PloS one Vol. 19; no. 4; p. e0301705
• Main Authors: Abuzaid, Dina, Al Ghour, Samer, Naghi, Monia
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 10.04.2024; Public Library of Science (PLoS)
• Subjects: Biology and Life Sciences; Computer and Information Sciences; Engineering and Technology; Physical Sciences; Social Sciences
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0301705

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.