STRONG FORM OF PRE-I-CONTINUOUS FUNCTIONS

In this paper, semiopen and pre-I-open sets used to define and investigate a new class of functions called strongly pre-I-continuous. Relationships between the new class and other classes of functions are established

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  • M. E. Abd El-Monsef, E. F. Lashien and A. A. Nasef, On I-open sets and I-continuous functions, Kyungpook Math. J., 32(1992), 21-30.
  • M. E. Abd El-Monsef, E. F. Lashien and A. A. Nasef, S-compactness via ideals, Tamkang J. Math., 24(4)(1993), 431-443.
  • M. E. Abd El-Monsef, R. A. Mahmoud and A. A. Nasef, Strongly semi-continuous functions, Arab J. Phys. Math., 11(1990).
  • A. Acikgoz, S. Yuksel and T. Noiri, I-preirresolute functions and I-preirresolute func- tions, Bull. Malays. Math. Sci. Soc., (2)(28)(1)(2005), 1-8.
  • Y. Beceren and T. Noiri, Strongly precontinuous functions, Acta Math. Hungar., 108(1- )(2005), 47-53.
  • D. A. Carnahan, Some properties related to compactness in topological spaces, Ph.D. Thesis, Univ. of Arkansas, 1973.
  • S. G. Crossley and S. K. Hildrebrand, Semi-closure, Texas J. Sci., 22(1971), 99-112.
  • S. G. Crossley and S. K. Hildreband, Semi-topological spaces, Fund. Math., 74(3)(1972), 254.
  • J. Dontchev, Idealization of Ganster-Reilly decomposition theorems, preprint. J. Dontchev, On pre-I-open sets and a decomposition of I-continuity, Banyan Math. J., (1996).
  • R. L. Ellis, A non-archimedean analogue of the Tietz Urysohn extension theorem, Nederl. Akad. Wetensch. Proc. Ser. A., 70(1967), 332-333.
  • E. Hatir and T. Noiri, On decompositions of continuity via idealization, Acta Math. Hungar., (4)(2002), 341-349.
  • E. Hayashi, Topologies de…ned by local properties, Math. Ann., 156(1964), 205-215.
  • D. Jankovic and T. R. Hamlett, New topologies from old via ideals, American Math. Monthly, (1990), 295-310.
  • A. Keskin and S. Yuksel, On K. Kuratowski, Topology, Academic Press, New York, 1966.
  • N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, spaces, JFS, 29(2006), 12-24. (1963), 36-41.
  • S. N. Maheshwari and R. Prasad, On s-normal spaces, Bull. Math. Soc. Sci. Math. R. S. Roumanie N. S., 70(1978), 27.
  • S. N. Maheshwari and R. Prasad, On s-regular spaces, Glasnik Mat., 30(1975), 347-350.
  • S. N. Maheshwari and R. Prasad, Some new separation axioms, Ann. Soc. Sci. Bruxelles, (1975), 395-402.
  • A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deep, On pre-continuous and weak pre-continuous mappings, Proc. Math. Phys. Soc. Egypt, 53(1982), 47-53.
  • R. L. Newcomb, Topologies which are compact modulo an ideal, Ph.D. Thesis, University of California, USA (1967).
  • T. Noiri, Remarks on semi-open mappings, Bull. Calcutta Math. Soc., 65(1973), 197-201.
  • V. Pipitone and G. Russo, Spazi semiconnessi e spazi semiaperti, Rend. Circ. Mat. Palermo, (2)24(1975), 273-385.
  • R. Vaidyanatahswamy, The localisation theory in set topology, Proc. Indian Acad. Sci., (1945), 51-61.
  • S. Yuksel, A. Acikgoz and E. Gursel, A new type of continuous functions in ideal topological space, to appear in J. Indian Acad. Math. S. Yuksel, T. Noiri and A. Acikgoz, On strongly I-continuous functions, Far. East J. Math., (1)(2003), 1-8.
  • Current address : J. Bhuvaneswari: Department of Computer Applications Rajalakshmi En- gineering College Thandalam, Chennai-602 105 TamilNadu, INDIA,, N. Rajesh: Department of Mathematics Kongu Engineering College Perundurai, Erode-638 052 Tamilnadu, INDIA,, A. Ke- skin: Selcuk University Faculty of Sciences and Arts, Department of Mathematics 42075, Campus Konya, TURKEY
  • E-mail address : sai_jbhuvana@yahoo.co.in, nrajesh_topology@yahoo.co.in, akeskin@selcuk.edu.tr