An application to explore the progress of a nation using the emerging nano topological concepts via multiple ideals

Kamalpreet Kaur; Asha  Gupta

doi:10.5269/bspm.82018

Kamalpreet Kaur Punjab Engineering College (Deemed to be University), Chandigarh https://orcid.org/0000-0003-3822-9516
Asha Gupta Department of Mathematics, Punjab Engineering College (Deemed to be University), Chandigarh, 160012, India https://orcid.org/0000-0002-2519-9517

DOI: https://doi.org/10.5269/bspm.82018

Abstract

The idea of nano topology was constituted by M.L. Thivagar wherein topology was generated using an intriguing methodology of approximation of rough sets. As the approach of approximation using the multiple ideals gives a higher value of accuracy when compared to the existing notions, the objective of this paper is to propose the nearly open forms of j-multi ideal nano topology, such as j-multi ideal nano semi-open, j-multi ideal nano pre-open, j-multi ideal nano regular open and j-multi ideal nano $\alpha$ open sets. An interrelation of all these open forms is illustrated. Various nano continuities using multi-ideal approximation technique are introduced and their interconnection is studied. Some nano separation axioms using this ideology are defined. A real-life example of nano topology is also discussed towards the end of this paper to find the key factors that govern the development or underdevelopment of a nation.

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Author Biographies

Kamalpreet Kaur, Punjab Engineering College (Deemed to be University), Chandigarh

Kamalpreet Kaur is faculty at the Department of Mathematics, Punjab Engineering College, Chandigarh (Deemed to be University). She did her PhD from Punjab Engineering College, Chandigarh(Deemed to be University) and MSc in mathematics from Punjabi University, Patiala, Punjab, India. Her research interests include general topology, nano topology, rough set theory, soft computing, and decision-making. She has had the opportunity of presenting her work at national and international conferences and workshops, where she engaged with fellow scholars, exchanged ideas, and received valuable feedback. Additionally, her previous research findings have been published in esteemed peer-reviewed journals, contributing to her field.

Asha Gupta, Department of Mathematics, Punjab Engineering College (Deemed to be University), Chandigarh, 160012, India

Asha Gupta is Professor and Head at the Department of Mathematics, Punjab Engineering College, Chandigarh(Deemed to be University) has teaching experience of more than thirty years. She was awarded ISCA (Indian Science Congress Association ) Young Scientist Award, got published two books and around 40 research papers in reputed national and International journals some of which are SCIE indexed. She also presented papers at national and International conferences including AIP. She has guided five Ph.Ds and three are in progress. Her research interests include General Topology, Fuzzy Topology, Nano Topology, Rough set theory, Soft computing, and Decision-making.