New soft separation axioms and fixed soft points with respect to total belong and total non-belong relations

Al-shami T. M., TERCAN A., Mhemdi A.

DEMONSTRATIO MATHEMATICA, vol.54, no.1, pp.196-211, 2021 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1515/dema-2021-0018
  • Journal Name: DEMONSTRATIO MATHEMATICA
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Linguistic Bibliography, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.196-211
  • Keywords: soft pre-open set, tt-soft pre Ti-space, extended soft topology, soft hyperconnected space, additive property, topological property, soft pre-compact space, pre-fixed soft point, SETS, COMPACT
  • Hacettepe University Affiliated: Yes

Abstract

In this article, we exploit the relations of total belong and total non-belong to introduce new soft separation axioms with respect to ordinary points, namely tt-soft pre T-i (i = 0, 1, 2, 3, 4) and tt-soft pre-regular spaces. The motivations to use these relations are, first, cancel the constant shape of soft preopen and pre-closed subsets of soft pre-regular spaces, and second, generalization of existing comparable properties on classical topology. With the help of examples, we show the relationships between them as well as with soft pre T-i (i = 0, 1, 2, 3, 4) and soft pre-regular spaces. Also, we explain the role of soft hyperconnected and extended soft topological spaces in obtaining some interesting results. We characterize a tt-soft pre-regular space and demonstrate that it guarantees the equivalence of tt-soft pre T-i (i = 0, 1, 2). Furthermore, we investigate the behaviors of these soft separation axioms with the concepts of product and sum of soft spaces. Finally, we introduce a concept of pre-fixed soft point and study its main properties.