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On iterate minimal structures and M-iterate continuous functions

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Języki publikacji
EN
Abstrakty
EN
We introduce the notion of mIT-structures determined by operators mint and mCl on an m-space (X, mX). By using mIT-structures, we introduce and investigate a function f : (X, mIT) → (Y, mY) called MIT-continuous. As special cases of M/T -continuity, we obtain M-semicontinuity [21] and M-precontinuity [23].
Rocznik
Tom
Strony
109--119
Opis fizyczny
Bibliogr. 30 poz.
Twórcy
autor
  • 2949-1 Shiokita-cho, Hinagu Yatsushiro-shi, Kumamoto-ken 869-5142, Japan, t.noiri@nifty.com
autor
  • Department of Mathematics Univ. Vasile Alecsandri of BacSu 600 115 BacSu, Rumania, vpopa@ub.ro
Bibliografia
  • [1] Abd El-Monsef M.E., El-Deeb S.N., Mahmoud R.A., ,β-open sets and β-continuous mappings, Bull. Fac. Sci. Assiut Univ., 12(1983), 77-90.
  • [2] Abd El-Monsef M.E., Mahmoud R.A., Lashin E.R., β-closure and β-interior, J. Fac. Ed. Ain Shams Univ., 10(1986), 235-245.
  • [3] Andrijevic D., Semi-preopen sets, Mat. Vesnik, 38(1986), 24-32.
  • [4] Andrijevic D., On b-open sets, Mat. Vesnik, 48(1996), 59-64.
  • [5] Boonpok C., Almost and weakly M-continuous functions in m-spaces, Far East J. Math. Sci., 43(2010), 41-58.
  • [6] Crossley S.G., Hildebrand S.K., Semi-closure, Texas J. Sci., 22(1971), 99-112.
  • [7] Crossley S.G., Hildebrand S.K., Semi-topological properties, Fund. Math., 74(1972), 233-254.
  • [8] Ekici E., Caldas M., Slightly y-continuous functions, Bol. Soc. Paran. Mat., 22(2004), 63-74.
  • [9] El-Atik A.A., A Study of Some Types of Mappings on Topological Spaces, M. Sci. Thesis, Tanta Univ., Egypt, 1997.
  • [10] El-Deeb S.N., Hasanein I.A., Mashhour A.S., Noiri T., On p-regular spaces, Bull. Math. Soc. Sci. Math. R. S. Roumanie, 27(75)(1983), 311-315.
  • [11] Levine N., Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36-41.
  • [12] Maheshwari S.N., Jain P.C., Some new mappings, Mathematica (Cluj), 24(47)(1982), 53-55.
  • [13] Maheshwari S.N., Thakur S.S., On a-irresolute mappings, Tamkang J. Math., 11(1980), 209-214.
  • [14] Mahmoud R.A., Abd El-Monsef M.E., β-irresolute and β-topological in variants, Proc. Pakistan Acad. Sci., 27(1990), 285-296.
  • [15] Maki H., Rao C.K., Nagoor Gani A., On generalizaing semi-open and preopen sets, Pure Appl. Math. Sci., 49(1999), 17-29.
  • [16] Mashhour A.S., Abd El-Monsef M.E., El-Deep S.N., On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 53(1982), 47-53.
  • [17] Mashhour A.S., Abd El-Monsef M.E., Hasanein I.A., On pretopologi- cal spaces, Bull. Math. Soc. Sci. Math. R. S. Roumanie, 28(76)(1984), 39-45.
  • [18] Mashhour A.S., Hasanein I.A., El-Deeb S.N., α-continuous and α-open mappings, Acta Math. Hungar., 41(1983), 213-218.
  • [19] Min W.K., m-semiopen sets and M-semicontinuous functions on spaces with minimal structures, Honam Math. J., 31(2009), 239-245.
  • [20] Min W.K., αm-open sets and αM-continuous functions, Commun. Korean Math. Soc., 25(2010), 251-256.
  • [21] Min W.K., On minimal semicontinuous functions, Commun. Korean Math. Soc., 27(2)(2012), 341-345.
  • [22] Min W.K., Kim Y.K., m-preopen sets and M-precontinuity on spaces with minimal structures, Adv. Fuzzy Sets Systems, 4(2009), 237-245.
  • [23] Min W.K., Kim Y.K., On minimal precontinuous functions, J. Chungcheong Math. Soc., 24(4)(2009), 667-673.
  • [24] Njastad O., On some classes of nearly open sets, Pacific J. Math., 15(1965), 961-970.
  • [25] Noiri T., Popa V., A generalization of some forms of g-irresolute functions, Eur. J. Pure Appl. Math., 2(2009), 473-493.
  • [26] Popa V., Noiri T., On M-continuous functions, Anal. Univ. ”Dunarea de Jos” Galati, Ser. Mat. Fiz. Mec. Teor., Fasc. II, 18(23) (2000), 31-41.
  • [27] Popa V., Noiri T., On the definitions of some generalized forms of continuity under minimal conditions, Mem. Fac. Sci. Kochi Univ. Ser. Math., 22(2001), 9-18.
  • [28] Popa V., Noiri T., A unified theory of weak continuity for functions, Rend Circ. Mat. Palermo (2), 51(2002), 439-464.
  • [29]Reilly I.L., Vamanamurthy M.K., On α-continuity in topological spaces, Acta Math. Hungar., 45(1985), 27-32.
  • [30] Rosas E., Rajesh N., Carpintero C., Some new types of open and closed sets in minimal structures, I, II, Int. Math. Forum, 4(2009), 2169-2184, 2185-2198.
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Bibliografia
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