On a type of generalized open sets

• Roy, Bishwambhar ^[1]
  1. [1] Women's Christian College
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 12, Nº. 2, 2011, págs. 163-173
• Idioma: inglés
• DOI: 10.4995/agt.2011.1649
• Enlaces
  • Texto completo
• Resumen

  • In this paper, a new class of sets called μ-generalized closed (briefly μg-closed) sets in generalized topological spaces are introduced and studied. The class of all μg-closed sets is strictly larger than the class of all μ-closed sets (in the sense of Á. Császár). Furthermore, g-closed sets (in the sense of N. Levine) is a special type of μg-closed sets in a topological space. Some of their properties are investigated here. Finally, some characterizations of μ-regular and μ-normal spaces have been given.

• Referencias bibliográficas
  • M. E. Abd El-Monsef, S. N. El-Deeb and R. A. Mahmoud, B-open sets and B-continuous mappings, Bull. Fac. Sci. Assiut Univ. 12 (1983), 77–90.
  • S. P. Arya and T. M. Nour, Characterizations of s-normal spaces, Indian J. Pure Appl. Math. 21, no. 8 (1990), 717–719.
  • Y. Beceren and T. Noiri, Some functions defined by semi-open sets and B-open sets, Chaos Solitons Fractals 36 (2008), 1225–1231. http://dx.doi.org/10.1016/j.chaos.2006.07.057
  • P. Bhattacharyya and B. K. Lahiri, Semi-generalized closed sets in topology, Indian J. Math. 29 (1987), 376–382.
  • M. Caldas, T. Fukutake, S. Jafari and T. Noiri, Some applications of d-preopen sets in topological spaces, Bull. Inst. Math. Acad. Sinica...
  • M. Caldas, D. N. Georgiou and S. Jafari, Characterizations of low separation axioms via a-open sets and a-closure operator, Bull. Soc. Paran....
  • M. Caldas, D. N. Georgiou and T. Noiri, More on -semiopen sets, Note di Mathematica
  • , no. 2 (2003), 113–126.
  • M. C. Caldas and S. Jafari, On d D-sets and associated weak separation axioms, Bull. Malaysian Math. Soc. 25 (2002), 173–185.
  • Á. Császár, Generalized topology, generalized continuity, Acta Math. Hungar. 96 (2002), 351–357. http://dx.doi.org/10.1023/A:1019713018007
  • Á. Császár, Generalized open sets in generalized topologies, Acta Math. Hungar. 106 (2005), 53–66. http://dx.doi.org/10.1007/s10474-005-0005-5
  • Á. Császár, d- and 0-modifications of generalized topologies, Acta Math. Hungar. 120 (2008), 275–279. http://dx.doi.org/10.1007/s10474-007-7136-9
  • Á. Császár, Normal generalized topologies, Acta Math. Hungar. 115, no. 4 (2007), 309– 313. http://dx.doi.org/10.1007/s10474-007-5249-9
  • J. Dontchev, I. Arokiarani and K. Balachandran, On generalized d-closed sets and almost weakly Hausdroff spaces, Questions Answers Gen. Topology...
  • C. Dorsett, Semi normal spaces, Kyungpook Math. J. 25(1985), 173–180.
  • C. Dorsett, Semi regular spaces, Soochow J. Math. 8 (1982), 45–53.
  • J. Dugunji, Topology, Allyn and Bacon, Boston, 1966.
  • E. Ekici, On y-normal spaces, Bull. Math. Soc. Sci. Math. Roumanie 50 (98) (2007), 259–272.
  • E. Ekici, On almost ngp-continuous functions, Chaos Solitons Fractals 32 (2007), 1935– 1944. http://dx.doi.org/10.1016/j.chaos.2005.12.056
  • S. Jafari and T. Noiri, On B-quasi irresolute functions, Mem. Fac. Sci. Kochi Univ.(Math.) 21 (2000), 53–62.
  • A. Kar and P. Bhattacharyya, Bitopological a-compact spaces, Riv. Mat. Parma 7, no. 1 (2002), 159–176.
  • A. Keskin and T. Noiri, On bD-sets and associated separation axioms, Bull. Iran. Math. Soc. 35, no. 1 (2009), 179–198.
  • N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo 19 (1970), 89–96. http://dx.doi.org/10.1007/BF02843888
  • N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36–41. http://dx.doi.org/10.2307/2312781
  • S. N. Maheshwari and R. Prasad, On s-regular spaces, Glasnik Mat. 10 (30) (1975), 347–350.
  • H. Maki, J. Umehara and T. Noiri, Every topological space is pre-T1/2, Mem. Fac. Sci. Kochi Univ. Ser. A. Math. 17 (1996), 33–42.
  • H. Maki, J. Umehara and K. Yamamura, Characterizations of T1/2-spaces using generalized v-sets, Indian J. Pure Appl. Math. 19, no. 7 (1998),...
  • H. Maki, R. Devi and K. Balachandran, Associated topologies of generalizrd a-closed sets and a-generalized closed sets, Mem. Fac. Sci. Kochi...
  • H. Maki, R. Devi and K. Balachandran, Generalized a-closed sets in topology, Bull. Fukuoka Univ. Ed., Part-III 42 (1993), 13–21.
  • A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt 53 (1982),...
  • T. Noiri, Semi-normal spaces and some functions, Acta Math. Hungar. 65, no. 3 (1994), 305-311. http://dx.doi.org/10.1007/BF01875158
  • M. C. Pal and P. Bhattacharyya, Feeble and strong forms of preirresolute functions, Bull. Malaysian Math. Soc. 19 (1996), 63–75.
  • J. H. Park, D. S. Song and R. Saadati, On generalized d-semiclosed sets in topological spaces, Chaos Solitons Fractals 33 (2007), 1329–1338....
  • S. Raychaudhuri and M. N. Mukherjee, On d-almost continuity and d-preopen sets, Bull. Inst. Math. Acad. Sinica 21 (1993), 357–366.
  • P. Sivagami and D. Sivaraj, W and V- sets of generalized topologies, Scientia Magna 5, no. 1 (2009), 83–93.
  • N. V. Velicko, H-closed topological spaces, Mat. Sb. 70 (1966), 98–112.