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2023•Indian Journal of Science and TechnologyOpen access

A Note on Separation Axioms in Kasaj Topological Spaces

Muddassar Azam Sindhu, P. Sathishmohan, K Rajalakshmi

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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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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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Available 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

Key concepts: Separation axiom, Topological space, Separated sets, T1 space, Mathematics, Topological tensor product, Disjoint sets, Closed set

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