Single-Valued Pentapartitioned Neutrosophic Bi-Topological Spaces

Suman Das¹, Prasanna Poojary², Vadiraja Bhatta G. R.^3,*, Sunny Kumar Sharma⁴

¹Department of Mathematics, Tripura University, Agartala, 799022, Tripura, India.

^2,4Department of Mathematics, Manipal Institute of Technology Bengaluru, Manipal Academy of Higher Education, Manipal, India.

³Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India.

Emails: sumandas18842@gmail.com; poojary.prasanna@manipal.edu; poojaryprasanna34@gmail.com; sunny.sharma@manipal.edu

*Correspondence: vadiraja.bhatta@manipal.edu

Abstract

In this article, we present the notion of Single-Valued Pentapartitioned Neutrosophic Bi-Topological Space (SVPNBTS) as a generalization of Single-Valued Pentapartitioned Neutrosophic Topological Space (SVPNTS) and Neutrosophic Bi-Topological Space (NBTS). Besides, we study the different types of open set and closed set namely single-valued pentapartitioned neutrosophic bi-open set (SVPNBOS), single-valued pentapartitioned neutrosophic bi-closed set (SVPNBCS), single-valued pentapartitioned neutrosophic bi-semi-open set (SVPNBSOS), single-valued pentapartitioned neutrosophic bi-semi-closed set (SVPNBSCS), single-valued pentapartitioned neutrosophic bi-pre-open set (SVPNBPOS), single-valued pentapartitioned neutrosophic bi-pre-closed set (SVPNBPCS), single-valued pentapartitioned neutrosophic bi-b-open set (SVPNBb-OS), single-valued pentapartitioned neutrosophic bi-b-closed set (SVPNBb-CS), etc. via SVPNBTSs. Besides, we introduce the notion of pairwise SVPNOS, pairwise SVPNCS, pairwise SVPNSOS, pairwise SVPNSCS, pairwise SVPNPOS, pairwise SVPNPCS, pairwise SVPNb-OS, pairwise SVPNb-CS, and furnish few illustrative examples on them. Further, we investigate several properties of these classes of sets and prove some interesting results in the form of propositions, theorems, etc. via SVPNBTSs.

Keywords: SVPNBTS; Bi-open set; Bi-closed set; Bi-semi-open set; Bi-pre-open set; NBTS.