Characterization of Soft S-Open Sets in Bi-Soft Topological Structure Concerning Crisp Points

Arif Mehmood, Mohammed M. Al-Shomrani, Muhammad Asad Zaighum and Saleem Abdullah
Additional contact information
Arif Mehmood: Department of Mathematics & Statistics, Riphah International University, Sector I-14, Islamabad 44000, Pakistan
Mohammed M. Al-Shomrani: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Muhammad Asad Zaighum: Department of Mathematics & Statistics, Riphah International University, Sector I-14, Islamabad 44000, Pakistan
Saleem Abdullah: Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan

Mathematics, 2020, vol. 8, issue 12, 1-23

Abstract: In this article, a soft s-open set in soft bitopological structures is introduced. With the help of this newly defined soft s-open set, soft separation axioms are regenerated in soft bitopological structures with respect to crisp points. Soft continuity at some certain points, soft bases, soft subbase, soft homeomorphism, soft first-countable and soft second-countable, soft connected, soft disconnected and soft locally connected spaces are defined with respect to crisp points under s-open sets in soft bitopological spaces. The product of two soft axioms with respect crisp points with almost all possibilities in soft bitopological spaces relative to semiopen sets are introduced. In addition to this, soft (countability, base, subbase, finite intersection property, continuity) are addressed with respect to semiopen sets in soft bitopological spaces. Product of soft first and second coordinate spaces are addressed with respect to semiopen sets in soft bitopological spaces. The characterization of soft separation axioms with soft connectedness is addressed with respect to semiopen sets in soft bitopological spaces. In addition to this, the product of two soft topological spaces is ( space if each coordinate space is soft space, product of two sot topological spaces is (S regular and C regular) space if each coordinate space is (S regular and C regular), the product of two soft topological spaces is connected if each coordinate space is soft connected and the product of two soft topological spaces is (first-countable, second-countable) if each coordinate space is (first countable, second-countable).

Keywords: soft sets; soft topological space; soft s-open set; soft bitopological spaces; soft s-separation axioms; soft product space; soft connectedness and soft coordinate spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/12/2100/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/12/2100/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:12:p:2100-:d:450150

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().