Weaker Forms of Soft Regular and Soft T 2 Soft Topological Spaces

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

Mathematics, 2021, vol. 9, issue 17, 1-13

Abstract: Soft ? -local indiscreetness as a weaker form of both soft local countability and soft local indiscreetness is introduced. Then soft ? -regularity as a weaker form of both soft regularity and soft ? -local indiscreetness is defined and investigated. Additionally, soft ? - T 2 as a new soft topological property that lies strictly between soft T 2 and soft T 1 is defined and investigated. It is proved that soft anti-local countability is a sufficient condition for equivalence between soft ? -locally indiscreetness (resp. soft ? -regularity) and soft locally indiscreetness (resp. soft ? -regularity). Additionally, it is proved that the induced topological spaces of a soft ? -locally indiscrete (resp. soft ? -regular, soft ? - T 2 ) soft topological space are (resp. ? -regular, ? - T 2 ) topological spaces. Additionally, it is proved that the generated soft topological space of a family of ? -locally indiscrete (resp. ? -regular, ? - T 2 ) topological spaces is soft ? -locally indiscrete and vice versa. In addition to these, soft product theorems regarding soft ? -regular and soft ? - T 2 soft topological spaces are obtained. Moreover, it is proved that soft ? -regular and soft ? - T 2 are hereditarily under soft subspaces.

Keywords: soft local indiscreetness; soft regularity; soft T2 soft topological spaces; soft product; soft subspace; soft generated soft topological space; soft induced topological spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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