Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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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)
  • Received : 2021.03.12
  • Accepted : 2021.07.06
  • Published : 2021.09.30
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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.

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References

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