∆-normal spaces and decompositions of normality

Ananga Kumar Das


Generalizations of normality, called (weakly) (functionally) ∆-normal spaces are introduced and their interrelation with some existing notions of normality is studied. ∆-regular spaces are introduced which is a generalization of seminormal, semiregular and θ-regular space. This leads to decompositions of normality in terms of ∆-regularity, seminormality and variants of ∆-normality.


δ-open sets; δ-closed sets (Weakly) (functionally) θ-normal spaces; (weakly) (functionally) ∆-normal spaces; θ-regular spaces; seminormalspaces

Full Text:



A. Csaszar, General Topology, Adam Higler Ltd, Bristol, 1978.

A.S. Davis, Indexed systems of neighbourhoods for general topological spaces, Amer. Math. Monthly 68 (1961), 886-893. https://doi.org/10.2307/2311686

R.F. Dickman, Jr. and J.R. Porter, -perfect and -absolutely closed functions, Illinois J. Math. 21 (1977), 42-60. https://doi.org/10.1215/ijm/1256049499

J.E. Joseph, -closure and -subclosed graphs, Math. Chron. 8 (1979), 99-117.

J.K. Kohli and A.K. Das, On functionally -normal spaces, Applied Gen. Topol. 6(2005), no. 1, 1-14. https://doi.org/10.4995/agt.2005.1960

J.K. Kohli and A.K. Das, New normality axioms and decompositions of normality, Glasnik Mat. 37 (2002), no. 57, 163-173.

J.K. Kohli and A.K. Das, A class of spaces containing all generalized absolutely closed (almost compact) spaces, Applied Gen. Topol. 7(2006), no. 2, 233-244. https://doi.org/10.4995/agt.2006.1926

J.K. Kohli and D. Singh, Weak normality properties and factorizations of normality, Acta. Math. Hungar. 110 (2006), no. 1-2, 67-80. https://doi.org/10.1007/s10474-006-0007-y

C. Kuratowski, Topologie I, Hafner, New York, 1958.

J.Mack, Countable paracompactness and weak normality properties, Trans. Amer.Math. Soc. 148 (1970), 265-272. https://doi.org/10.1090/S0002-9947-1970-0259856-3

M. Mrsevic and D. Andrijevic On -connectedness and closure spaces, Topology Appl. 123 (2002), 157-166. https://doi.org/10.1016/S0166-8641(01)00179-1

M.K. Singal and S.P. Arya, On almost regular spaces, Glasnik Mat. 4 (1969), no. 24, 89-99.

M.K. Singal and S.P. Arya, On almost normal and almost completely regular spaces, Glasnik Mat. 5 (1970), no. 25, 141-152.

M.K. Singal and A. Mathur, On nearly compact spaces, Boll. U.M.I. 4 (1969), 702-710.

M.K. Singal and A.R. Singal, Mildly normal spaces, Kyungpook Math J. 13 (1973), 27-31.

E.V. Stchepin, Real valued functions and spaces close to normal, Sib. J. Math. 13 (1972), no. 5, 1182-1196. https://doi.org/10.1007/BF00968394

N.V. Velicko H-closed topological spaces, Amer. Math. Soc, Transl. 78 (1968), no. 2, 103-118. https://doi.org/10.1090/trans2/078/05

G. Vigilino, Seminormal and C-compact spaces, Duke J. Math. 38 (1971), 57-61. https://doi.org/10.1215/S0012-7094-71-03808-7

Abstract Views

Metrics Loading ...

Metrics powered by PLOS ALM


Cited-By (articles included in Crossref)

This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site

1. On relative β-normality
A. K. Das, S. S. Raina
Acta Mathematica Hungarica  vol: 160  issue: 2  first page: 468  year: 2020  
doi: 10.1007/s10474-019-01006-4

2. On permutable pairs of quasi-uniformities
Maria João Ferreira, Mack Matlabyana, Jorge Picado
Topology and its Applications  vol: 196  first page: 260  year: 2015  
doi: 10.1016/j.topol.2015.10.004

3. Some new higher separation axioms via sets having non-empty interior
Pratibha Bhat, Ananga Kumar Das, Lishan Liu
Cogent Mathematics  vol: 2  issue: 1  first page: 1092695  year: 2015  
doi: 10.1080/23311835.2015.1092695

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt