∆-normal spaces and decompositions of normality

• Das, A.K. ^[1]
  1. [1] Shri Mata Vaishno Devi University

     Shri Mata Vaishno Devi University

     India

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 10, Nº. 2, 2009, págs. 197-206
• Idioma: inglés
• DOI: 10.4995/agt.2009.1733
• Enlaces
  • Texto completo
• Resumen

  • 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.

• Referencias bibliográficas
  • 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),...
  • 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