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

Ankit Gupta, Ratna Dev Sarma

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.


Keywords


normality; regularity; generalized topology; Urysohn's lemma, Partition of Unity; $\theta$-normality

Subject classification

54A05; 54D10

Sponsor(s)



Full Text:

PDF

References


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. (Google Scholar)

A ́. Csa ́sz ́ar, Generalized open sets, Acta Math. Hungar., 75 (1-2) (1997), 65–87. (Google Scholar)

A. K. Das, ∆-normal spaces and decompositions of normality, App. Gen. Top. 10 (2) (2009), 197–206. (Google Scholar)

Dickman, R. F., Jr.; Porter, Jack R. θ-perfect and θ-absolutely closed functions, Illinois J. Math. 21 (1) (1977), 42–60. (Google Scholar)

J. Dugundji, Topology, Allyn and Bacon, Boston, 1972. (Google Scholar)

A. Gupta and R. D. Sarma, On m-open sets in topology, conference proceeding APMSCSET- 2014, page no. 7–11. (Google Scholar)

J. K. Kohli and A. K. Das, New normality axioms and decompositions of normality, Glasnik Mat. 37 (57) (2002), 163-–173. (Google Scholar)

N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Month. 70 (1963), 36–41. (Google Scholar)

A. S. Mashhour, M. E. Abd EI-Monsef and S. N. El-Deeb, On pre-continuous and weak pre-continuous mappings, Proc. Math. and Phys. Soc. Egypt. 53 (1982), 47–53. (Google Scholar)

O. Nja ̆stad, On some classes of nearly open sets, Pacific J. Math. 15 (1965), 961–970. (Google Scholar)

N.V. Veliˇcko, H-closed topological spaces, Amer. Math. Soc, Transl. 78 (2) (1968), 103-–1180. (Google Scholar)


Refbacks

  • There are currently no refbacks.


ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr