Two New Types of Irresolute Functions via -open Sets

Two New Types of Irresolute Functions via -open Sets

The main purpose of this paper is to introduce two new types of irresolute functions called completely irresolute and completely weakly -irresolute functions via -open sets introduced by Ekici. We obtain some characterizations of these functions. Also, we investigate some fundamental properties between these new notions and separation and covering

___

  • [1] Abd El-Monsef, M.E.; El-Deep, S.N.; Mohmoud, R.A. ?-open sets and ?-continuous mappings. Bulletin of the Faculty of Science Assiut University. 1983; 12, 77-90.
  • [2] Arya, S.P.; Gupta, R. On strongly continuous maps. Kyungpook Mathematical Journal. 1974; 14, 131-143.
  • [3] Allam, A.A.; Zaharan, A.M.; Hasanein, I.A. On almost continuous, ?-continuous and set connected mappings. Indian Journal of Pure and Applied Mathematics. 1987; 18(11), 991-996.
  • [4] Ergun, N. On nearly paracompact spaces. Istanbul Universitesi Fen Fakültesi Mecmuası A Serisi. 1980; 45, 65-87.
  • [5] Ekici, E. Generalization of perfectly continuous, regular set-connected and clopen functions. Acta Mathematica Hungarica. 2005; 107(3), 193-206.
  • [6] Ekici, E. New forms of contra continuity. Carpathian Journal of Mathematics. 2008; 24(1), 37-45.
  • [7] Ekici, E. On ?-open sets, ??∗ -sets and ??ℰ ∗ -sets and decompositions of continuity. Arabian Journal for Science and Engineering. 2008; 33(2A), 269-281.
  • [8] Ekici, E. Some weak forms of ?-continuity and ? ∗ - first-countable spaces (submitted)
  • [9] Levine, N. Strong continuity in topological spaces. The American Mathematical Monthly. 1960; 67, 269.
  • [10] Long, P.E.; Herrington, L.L. Basic properties of regular-closed functions. Rendiconti del Circolo Matematico di Palermo. 1978; 27, 20-28.
  • [11] Maio, G.D. ?-closed spaces, ?-sets and ?- continuous functions. Accademia delle Scienze di Torino. 1984; 118, 125-134.
  • [12] Singal, M.K.; Singal, A. Almost continuous mappings. Yokohama Mathematical Journal. 1968; 16, 63-73.
  • [13] Singal, M.K.; Arya, S.P. On almost regular spaces, Glasnik Matematicki. 1969; 4(24), 89-99.
  • [14] Singal, M.K.; Singal, A.R.; Mathur, A. On nearlycompact spaces. Bollettino dell’Unione Matematica Italiana. 1969; 4(2), 702-710.
  • [15] Singal, M.K.; Arya, S.P. Almost normal and almost completely regular spaces. Glasnik Matematicki. 1970; 5(25), 141-152.
  • [16] Staum, R. The algebra of bounded continuous functions into a nonarchimedean field. Pacific Journal of Mathematics. 1974; 50, 169-185.
  • [17] Stone, M.H. Applications of the theory of Boolean rings to general topology. Transaction of the American Mathematical Society. 1937; 41, 373-381.
  • [18] Thomson, T. ?-closed spaces. Proceeding of the American Mathematical Society. 1976; 60, 335-338.
  • [19] Velicko, N.V. ?-closed topological spaces. American Mathematical Society Translations Series 2. 1968; 78(2), 103-118.