Investigating Concepts in Soft Topological Structures through Subspaces

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 tau-neighborhood in a subspace S⊆X of any x∈S as ˜τ(x)∩S, noting that his definition of the τ-neighborhood in X of any x∈X is ˜τ(x), which equals τ(x)∩X. Moreover, this study researches some of the relations between concepts in a space and their correspondences in subspaces. Besides, it explores whether τ -C-, ˜τ-T-, ˜τ-B-, and ˜τ-I-soft discrete and indiscrete topologies is hereditary or not. Finally, this study handles if further research concerning these aspects is needed.