Soft Weakly Quasi-Continuous Functions Between Soft Topological Spaces

Samer Al-Ghour (), Dina Abuzaid and Monia Naghi
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Samer Al-Ghour: Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan
Dina Abuzaid: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Monia Naghi: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2024, vol. 12, issue 20, 1-19

Abstract: As an extension of quasi-continuity in general topology, we define soft quasi-continuity. We show that this notion is equivalent to the known notion of soft semi-continuity. Next, we define soft weak quasi-continuity. With the help of examples, we prove that soft weak quasi-continuity is strictly weaker than both soft semi-continuity and soft weak continuity. We introduce many characterizations of soft weak quasi-continuity. Moreover, we study the relationship between soft quasi-continuity and weak quasi-continuity with their analogous notions in general topology. Furthermore, we show that soft regularity of the co-domain of a soft function is a sufficient condition for equivalence between soft semi-continuity and soft weakly quasi-continuity. Furthermore, we provide several results of soft composition, restrictions, preservation, and soft graph theorems in terms of soft weak quasi-continuity.

Keywords: soft semi-continuity; quasi-continuity; weakly quasi-continuity; soft quasi-continuity; generated soft topology (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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