Soft Minimal Soft Sets and Soft Prehomogeneity in Soft Topological Spaces

• Published in: INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGENT SYSTEMS Vol. 21; no. 3; pp. 269 - 279
• Main Author: Ghour, Samer Al
• Format: Journal Article
• Language: English
• Published: 한국지능시스템학회 2021
• Subjects: 전기공학; Soft preopen soft sets; Prehomogeneity; Soft locally indiscrete; Generated soft topology; Soft minimal soft open sets
• ISSN: 1598-2645; 2093-744X
• DOI: 10.5391/IJFIS.2021.21.3.269

In this paper, we give characterizations for soft minimal soft open sets in terms of the soft closure operator, and we conclude that soft subsets of soft minimal soft open sets are soft preopen sets. In addition to these, we define soft minimal soft sets and soft minimal soft preopen sets as two new classes of soft sets in soft topological spaces, and we define soft prehomogeneity as a new soft topological property. We give several relationships regarding these new notions and related known soft topological notions. We show that soft minimal soft preopen sets are soft points, and we prove that soft minimal soft sets with non-null soft interiors are soft minimal soft open sets. Moreover, we show that soft prehomogeneous soft topological space that has a soft minimal soft set is soft locally indiscrete. Also, we give several characterizations of soft locally indiscrete soft topological space in terms of soft minimal soft open sets, soft minimal soft sets, soft preopen sets, and soft prehomogeneity. We deal with correspondence between our new soft topological notions and their analogs topological ones. Finally, we raise six open questions KCI Citation Count: 0