A Note on Separation Axioms in Kasaj Topological Spaces

M Sindhu; P Sathishmohan; K Rajalakshmi

doi:10.17485/IJST/v16i42.1508

Article

A Note on Separation Axioms in Kasaj Topological Spaces

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i42.1508

Year: 2023, Volume: 16, Issue: 42, Pages: 3764-3770

Original Article

A Note on Separation Axioms in Kasaj Topological Spaces

M Sindhu¹, P Sathishmohan^2*, K Rajalakshmi³

¹Research Scholar, Department of Mathematics, Kongunadu Arts and Science College (Autonomous), Coimbatore, 641 029, Tamil Nadu, India
²Assistant Professor, Department of Mathematics, Kongunadu Arts and Science College (Autonomous), Coimbatore, 641 029, Tamil Nadu, India
³Assistant Professor, Department of Science and Humanities, Sri Krishna College of Engineering and Techonology, Coimbatore, 641 029, Tamil Nadu, India

*Corresponding Author
Email: [email protected]

Received Date:19 June 2023, Accepted Date:26 September 2023, Published Date:13 November 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: The separation axioms are about the use of kasaj topological means to distinguish disjoint sets and distinct points and the purpose of this work is to investigate the spaces namely KSgp[KSgsp]-T0 spaces, KSgp[KSgsp]-T1 spaces, KSgp[KSgsp]-T2 spaces by utilizing KSgp[KSgsp]-open sets in Kasaj topological spaces. Also, we discuss their relationship with existing concepts in Kasaj topological spaces. Methods: Any two Kasaj topologically distinguishable points must be distinct, and any two separated points must be Kasaj topologically distinguishable. Finding: This study consists of three separation axioms namely -T0 spaces, -T1 spaces, -T2 spaces by utilizing -open sets in Kasaj topological spaces. Novelty: This study uses their relationship with existing concepts in Kasaj topological spaces. AMS Classification: 54A05,54B05,54A99.

Keywords: KSgp-T0 spaces; KSgsp-T0 space; KSgp-T1 spces; KSgsp-T1 spaces; KSgp-T2 spaces; KSgsp-T2 spaces

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Copyright

© 2023 Sindhu et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)