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http://dx.doi.org/10.11568/kjm.2021.29.3.501

A GENERALIZED APPROACH TOWARDS NORMALITY FOR TOPOLOGICAL SPACES  

Gupta, Ankit (Department of Mathematics, Bharati College, University of Delhi)
Sarma, Ratna Dev (Department of Mathematics, Bharati College, University of Delhi)
Publication Information
Korean Journal of Mathematics / v.29, no.3, 2021 , pp. 501-510 More about this Journal
Abstract
A uniform study towards normality is provided for topological spaces. Following Császár, 𝛄-normality and 𝛄(𝜃)-normality are introduced and investigated. For 𝛄 ∈ 𝚪13, 𝛄-normality is found to satisfy Urysohn's lemma and provide partition of unity. Several existing variants of normality such as 𝜃-normality, 𝚫-normality etc. are shown to be particular cases of 𝛄(𝜃)-normality. In this process, 𝛄-regularity and 𝛄(𝜃)-regularity are introduced and studied. Several important characterizations of all these notions are provided.
Keywords
normality; regularity; generalized topology; Urysohn's lemma; partition of unity; ${\theta}$-normality; ${\delta}$-normality.;
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