Investigating Concepts in Soft Topological Structures through Subspaces

Arslan B., Aydın T.

New Mathematics and Natural Computation, 2025 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2025
  • Doi Number: 10.1142/s1793005727500013
  • Journal Name: New Mathematics and Natural Computation
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: proximity mappings, Soft sets, τ̃-B- and τ̃-I-open sets, τ̃-B- and τ̃-I-soft subspace topologies, τ̃-C- and τ̃-T-closed sets, τ̃-C- and τ̃-T-soft subspace topologies
  • Çanakkale Onsekiz Mart University Affiliated: Yes

Abstract

Following the study of Molodtsov on soft topological structures in 2015, this study discusses the concepts in soft topological structures through subspaces, investigates some of their crucial properties, and provides their characterizations. To ensure consistency with Molodtsov’s framework, this paper defines the τ̃-neighborhood in a subspace S ⊆ X of any x ∈ S as τ̃(x) ∩ S, noting that his definition of the τ̃-neighborhood in X of any x ∈ X is τ̃(x), which equals τ̃(x) ∩ X. Moreover, this study researches some of the relations between concepts in a space and their correspondences in subspaces. Besides, it explores whether being τ̃-C-, τ̃-T-, τ̃-B-, and τ̃-I-soft discrete and indiscrete topologies is hereditary or not. Finally, this study handles if further research concerning these aspects is needed.