Abstract
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 t t tt -soft pre T i ( i = 0 , 1 , 2 , 3 , 4 ) {T}_{i}\hspace{0.33em}\left(i=0,1,2,3,4) and t t tt -soft pre-regular spaces. The motivations to use these relations are, first, cancel the constant shape of soft pre-open 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 ) {T}_{i}\hspace{0.33em}\left(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 t t tt -soft pre-regular space and demonstrate that it guarantees the equivalence of t t tt -soft pre T i ( i = 0 , 1 , 2 ) {T}_{i}\hspace{0.33em}\left(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.
Highlights
Soft set was established by Molodtsov [1], in 1999, as a new technique to approach real-life problems that suffer from vagueness and uncertainty
It means that the class of soft pre-open sets in a soft hyperconnected space (X, σ, M) constructs a new soft topology σpre over X containing σ
We have formulated the concepts of tt-soft pre Ti-spaces using the relations of total belong and total non-belong
Summary
Soft set was established by Molodtsov [1], in 1999, as a new technique to approach real-life problems that suffer from vagueness and uncertainty. In 2011, Shabir and Naz [5] as well as Çağman et al [6] employed soft sets to introduce the concept of soft topological space. They used two different methods to define soft topology. The authors of [17], in 2018, described the relations between an ordinary point and soft set by two new relations, namely partial belong and total non-belong According to these new relations, many soft topological concepts and notions were reformulated; as an example, see the different types of soft separation axioms given in [17,18,19]. We derive the sufficient conditions that keep pre-fixed soft points between a soft topological space and its parametric topological spaces
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
