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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

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

References

  1. M. E. Abd EI-Monsef, R. A. Mahmoud and S. N. El-Deeb, β - open sets and β - continuous mappings, Bull. Fac. Sci. Assiut Univ. 12 (1983), 77-90.
  2. A. Csaszar, Generalized open sets, Acta Math. Hungar., 75 (1-2) (1997), 65-87. https://doi.org/10.1023/A:1006582718102
  3. A. K. Das, Δ-normal spaces and decompositions of normality, App. Gen. Top. 10 (2) (2009), 197-206. https://doi.org/10.4995/agt.2009.1733
  4. Dickman, R. F., Jr.; Porter, Jack R. θ-perfect and θ-absolutely closed functions, Illinois J. Math. 21 (1) (1977), 42-60. https://doi.org/10.1215/ijm/1256049499
  5. J. Dugundji, Topology, Allyn and Bacon, Boston, 1972.
  6. A. Gupta and R. D. Sarma, On m-open sets in topology, conference proceeding APMSCSET2014, page no. 7-11.
  7. J. K. Kohli and A. K. Das, New normality axioms and decompositions of normality, Glasnik Mat. 37 (57) (2002), 163--173.
  8. N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Month. 70 (1963), 36-41. https://doi.org/10.1080/00029890.1963.11990039
  9. A. S. Mashhour, M. E. Abd EI-Monsef and S. N. El-Deeb, On pre-continuous and weak precontinuous mappings, Proc. Math. and Phys. Soc. Egypt. 53 (1982), 47-53.
  10. O. Njastad, On some classes of nearly open sets, Pacific J. Math. 15 (1965), 961-970. https://doi.org/10.2140/pjm.1965.15.961
  11. N.V. Velicko, H-closed topological spaces, Amer. Math. Soc, Transl. 78 (2) (1968), 103--118.