Somewhat omega continuity and somewhat omega openness in soft topological spaces

Article type: Research Article

Authors: Al Ghour, Samer^{; *}

Affiliations: Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan

Correspondence: [*] Corresponding author. Samer Al Ghour. E-mail: algore@just.edu.jo..

Abstract: In this paper, we introduce soft somewhat ω-continuous soft mappings and soft somewhat ω-open soft mappings as two new classes of soft mappings. We characterize these two concepts. Also, we prove that the class of soft somewhat ω-continuous (resp. soft somewhat ω-open) soft mappings contains the class of soft somewhat continuous (resp. soft somewhat open) soft mappings. Moreover, we obtain some sufficient conditions for the composition of two soft somewhat ω-continuous (resp. soft somewhat ω-open) soft mappings to be a soft somewhat ω-continuous (resp. a soft somewhat ω-open) soft mapping. Furthermore, we introduce some sufficient conditions for restricting a soft somewhat ω-continuous (resp. soft somewhat ω-open) soft mapping to being a soft somewhat ω-continuous (resp. soft somewhat ω-open) soft mapping. In addition to these, we introduce extension theorems regarding soft somewhat ω-continuity and soft somewhat ω-openness. Finally, we investigate the correspondences between the novel notions in soft topology and their general topological analogs.

Keywords: Soft somewhat continuous soft mapping, soft ω-continuous soft mappings, soft somewhat open soft mapping, soft generated soft topological space

DOI: 10.3233/JIFS-222098

Journal: Journal of Intelligent & Fuzzy Systems, vol. 44, no. 1, pp. 1385-1396, 2023