Authors:
Ahmad Al-Omari Faculty of Sciences, Department of Mathematics, Al al-Bayt University, P.O. Box 130095, Mafraq 25113, Jordan

Search for other papers by Ahmad Al-Omari in
Current site
Google Scholar
PubMed
Close
and
Takashi Noiri 2949-1 Shiokita-cho, Hinagu, Yatsushiro-shi, Kumamoto-ken, 869-5142, Japane-mail: t.noiri@nifty.com

Search for other papers by Takashi Noiri in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

A new kind of sets called generalized w-closed (briefly gw-closed) sets is introduced and studied in a topological space by using the concept of weak structures introduced by Á. Császár in [6]. The class of all gw-closed sets is strictly larger than the class of all w-closed sets. Furthermore, g-closed sets (in the sense of N. Levine [17]) is a special type of gw-closed sets in a topological space. Some of their properties are investigated. Finally, some characterizations of w-regular and w-normal spaces have been given.

  • [1] Abd El-Monsef, M. E. Geaisa, A. N. Mahmoud, R. A. 1985 β-regular spaces Proc. Math. Phys. Soc. Egypt 60 4752.

  • [2] Abd El-Monsef, M. E. El-Deeb, S. N. Mahmoud, R. A. 1983 β-open sets and β-continuous mappings Bull. Fac. Sci. Assiut Univ. 12 7790.

    • Search Google Scholar
    • Export Citation
  • [3] Andrijević, D. 1986 Semi-preopen sets Mat. Vesnik 38 2432.

  • [4] Andrijević, D. 1996 On b-open sets Mat. Vesnik 48 5964.

  • [5] Arya, S. P. Nour, T. 1990 Characterizations of s-normal spaces Indian J. Appl. Math. 21 717719.

  • [6] Császár, Á. 2011 Weak structures Acta Math. Hungar. 131 193195 .

  • [7] Császár, Á. 2002 Generalized topology, generalized continuity Acta Math. Hungar. 96 351357 .

  • [8] Dontchev, J. 1995 On generalizing semi-preopen sets Mem. Fac. Sci. Kochi Univ. Ser. A, Math. 16 3548.

  • [9] Dontchev, J. Ganster, M. 1996 On δ-generalized closed sets and -spaces Mem. Fac. Sci. Kochi Univ. Ser. A, Math. 17 1531.

  • [10] Dunham, W. 1977 -space Kyunpook Math. J. 17 161169.

  • [11] Ekici, E. 2007 On γ-normal spaces Bull. Math. Soc. Sci. Math. Roumanie 50 98 259272.

  • [12] Ekici, E. Noiri, T. 2006 On a generalization of normal, almost normal and mildly normal spaces-I Math. Moravica 10 920.

  • [13] El-Deeb, S. N. Hasanein, I. A. Mashhour, A. S. Noiri, T. 1983 On p-regular spaces Bull. Math. Soc. Sci. Math. R.S. Roumanie (N.S.) 27 75 311315.

    • Search Google Scholar
    • Export Citation
  • [14] Ganster, M. Steiner, M. 2007 On -closed sets Appl. Gen. Topol. 8 243247.

  • [15] Kelley, J. L. 1955 General Topology Van Nostrand New York.

  • [16] Levine, N. 1963 Semi-open sets and semi-continuity in topological spaces Amer. Math. Monthly 70 3641 .

  • [17] Levine, N. 1970 Generalized closed sets in topology Rend. Circ. Mat. Palermo (2) 19 8996 .

  • [18] Maheshwari, S. N. Prasad, R. 1975 On s-regular spaces Glasnik Mat. Ser. III 10 30 347350.

  • [19] Maheshwari, S. N. Prasad, R. 1978 On s-normal spaces Bull. Math. Soc. Math. R.S. Roumanie. 22 70 2729.

  • [20] Mahmoud, R. A. Abd El-Monsef, M. E. 1990 β-irresolute and β-topological invariants Proc. Pakistan Acad. Sci. 27 285296.

  • [21] Maki, H. Devi, R. Balachandran, K. 1994 Associated topologies of generalized α-closed sets and α-generalized closed sets Mem. Fac. Sci. Kochi Univ. Ser. A, Math. 15 5163.

    • Search Google Scholar
    • Export Citation
  • [22] Mashhour, A. S. Abd El-Monsef, M. E. El-Deep, S. N. 1982 On precontinuous and weak precontinuous mappings Proc. Math. Phys. Soc. Egypt 53 4753.

    • Search Google Scholar
    • Export Citation
  • [23] Njåstad, O. 1965 On some classes of nearly open sets Pacific J. Math. 15 961970.

  • [24] Noiri, T. 2008 A unified theory for certain modifications of generalized closed sets Internat. J. General Topology 1 8799.

  • [25] Noiri, T. Popa, V. 2002 A unified theory of contra-continuity for functions Annal. Univ. Sci. Budapest 44 115137.

  • [26] Noiri, T. Roy, B. 2011 Unification of generalized open sets on topological spaces Acta Math. Hungar. 130 349357 .

  • [27] Nour, T. M., Contributions to the Theory of Bitopological Spaces, Ph.D. Thesis, Univ. of Delhi, 1989.

  • [28] Park, J. H. 2006 Strongly θ-b-continuous functions Acta Math. Hungar. 110 347359 .

  • [29] Park, J. H. Lee, B. Y. Son, M. J. 1997 On δ-semiopen sets in topological space J. Indian Acad. Math. 19 5967.

  • [30] Park, J. H. Park, Y. B. Lee, B. Y. 2002 On gp-closed sets and pre gp-continuous functions Indian J. Pure Appl. Math. 33 312.

  • [31] Park, J. H. Song, D. S. Saadati, R. 2007 On generalized δ-semiclosed sets in topological spaces Chaos Soliton Fractals 33 13291338 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [32] Popa, V. Noiri, T. 2000 On M-continuous functions Annal. Univ. “Dunarea de Jos” Galati, Ser. Mat. Fiz. Mec. Teor. 18 23 3141.

    • Search Google Scholar
    • Export Citation
  • [33] Popa, V. Noiri, T. 2001 On the definitions of some generalized forms of continuity under minimal conditions Mem. Fac. Sci. Kochi Univ. Ser. A, Math. 22 3141.

    • Search Google Scholar
    • Export Citation
  • [34] Raychaudhuri, S. Mukherjee, M. N. 1993 On δ-almost continuity and δ-preopen sets Bull. Inst. Math. Acad. Sinica 21 357366.

  • [35] Veličko, N. V. 1968 H-closed topological spaces Amer. Math. Soc. Transl., (2) 78 103118.

  • Collapse
  • Expand

To see the editorial board, please visit the website of Springer Nature.

Manuscript Submission: HERE

For subscription options, please visit the website of Springer Nature.

Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia  
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
May 2024 46 0 0
Jun 2024 29 0 0
Jul 2024 26 0 0
Aug 2024 10 0 0
Sep 2024 43 0 0
Oct 2024 25 0 0
Nov 2024 3 0 0