Korean J. Math. Vol. 29 No. 3 (2021) pp.501-510
DOI: https://doi.org/10.11568/kjm.2021.29.3.501

A generalized approach towards normality for topological spaces

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Published: Sep 30, 2021
Keywords:
normality, regularity, generalized topology, Urysohn's lemma, Partition of Unity, $\theta$-normality
Mathematics Subject Classification:
54A05, 54D10

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Ankit Gupta
Department of Mathematics, Bharati College, University of Delhi Delhi 110058, India
Ratna Dev Sarma
Department of Mathematics, Rajdhnai College, University of Delhi Delhi 110015, India

Abstract

A uniform study towards normality is provided for topological spaces. Following Cs\'{a}sz\'{a}r, $\gamma$-normality and $\gamma$($\theta$)-normality are introduced and investigated. For $\gamma \in \Gamma_{13}$, $\gamma$-normality is found to satisfy Urysohn's lemma and provide partition of unity. Several existing variants of normality such as $\theta$-normality, $\Delta$-normality etc. are shown to be particular cases of $\gamma$($\theta$)-normality. In this process, $\gamma$-regularity and $\gamma$($\theta$)-regularity are introduced and studied. Several important characterizations of all these notions are provided.



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