Soft ? p -Open Sets and Soft ? p -Continuity in Soft Topological Spaces

Samer Al Ghour
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Samer Al Ghour: Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan

Mathematics, 2021, vol. 9, issue 20, 1-11

Abstract: We define soft ? p -openness as a strong form of soft pre-openness. We prove that the class of soft ? p -open sets is closed under soft union and do not form a soft topology, in general. We prove that soft ? p -open sets which are countable are soft open sets, and we prove that soft pre-open sets which are soft ? -open sets are soft ? p -open sets. In addition, we give a decomposition of soft ? p -open sets in terms of soft open sets and soft ? -dense sets. Moreover, we study the correspondence between the soft topology soft ? p -open sets in a soft topological space and its generated topological spaces, and vice versa. In addition to these, we define soft ? p -continuous functions as a new class of soft mappings which lies strictly between the classes of soft continuous functions and soft pre-continuous functions. We introduce several characterizations for soft pre-continuity and soft ? p -continuity. Finally, we study several relationships related to soft ? p -continuity.

Keywords: soft ? -open; soft pre-open sets; soft pre-continuity; generated soft topology; soft induced topological spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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