Separation Axioms of abga 􀀀 Closed Sets in Topological Spaces

K Suthi Keerthana; M Vigneshwaran; L Vidyarani

doi:10.17485/IJST/v17i11.135

Article

Separation Axioms of abga 􀀀 Closed Sets in Topological Spaces

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17i11.135

Year: 2024, Volume: 17, Issue: 11, Pages: 1028-1035

Original Article

Separation Axioms of abga 􀀀 Closed Sets in Topological Spaces

K Suthi Keerthana^1*, M Vigneshwaran², L Vidyarani²

¹Research Scholar, Department of Mathematics, Kongunadu Arts and Science College, Coimbatore, Tamil Nadu, India
²Assistant Professor, Department of Mathematics, Kongunadu Arts and Science College, Coimbatore, Tamil Nadu, India

*Corresponding Author
Email: [email protected]

Received Date:18 January 2024, Accepted Date:12 February 2024, Published Date:29 February 2024

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

Abstract

Objectives: The notion of the article is to introduce new spaces called - space, - space, - space by using - closed set. Methods: The characteristics and properties of the new spaces are explained using theorems and propositions. To prove the converse part of the theorems, counter examples are utilized. Findings: As the reverse implications of the theorems which explains the properties of the new spaces, are proved to be not true using the examples we could find the weaker and stronger spaces. Several of their fundamental characterizations and their relationships with other corresponding kinds of spaces are discussed. Novelty: The inter relationship between the spaces are identified and investigated and relation among the spaces are graphically illustrated. Independence relation among the - space, - space, - space and other existing spaces are identified. Several examples are discussed for the independence relation.

Keywords: - closed set; - open set; - spce; - space; - space

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Copyright

© 2024 Keerthana 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)