Real Analysis Exchange

On Generalized Continuous Multifunctions and Their Selections

D. K. Ganguly and Piyali Mallick

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In this paper a generalized concept of continuous multifunctions has been studied. The main goal of this paper is to study some properties concerning a new type of multifunction along with its selections.

Article information

Real Anal. Exchange Volume 33, Number 2 (2007), 449-456.

First available in Project Euclid: 18 December 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27}
Secondary: 54C08: Weak and generalized continuity

$\mathcal{E}$-cluster point $\mathcal{E}$-continuity quasicontinuity $B$-continuity Baire continuity $ B^{*}$-continuity semi-continuity subcontinuity weak-subcontinuity $\mathcal{E}$-cluster multifunction densely continuous form


Ganguly, D. K.; Mallick, Piyali. On Generalized Continuous Multifunctions and Their Selections. Real Anal. Exchange 33 (2007), no. 2, 449--456.

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  • C. Berge, Topological Spaces, Oliver and Boyd, London, 1963.
  • J. Cao & W. B. Moors, Quasicontinuous selections of upper continuous set-valued mappings, Real Anal. Exchange, 31(1) (2005/6), 63–72.
  • J. Ewert, Quasicontinuity of multi-valued maps with respect to the qualitative topology, Math Hung, 56 (1990), 39–44.
  • R. V. Fuller, Relations among continuous and various non-continuous functions, Pacific J. Math., 25 (1968), 495–509.
  • D. K. Ganguly & Chandrani Mitra, On some weaker forms of $B^{*}$ continuity for multifunctions, Soochow J. Math., 32(1) (2006), 59–69.
  • S. T. Hammer & R. A. McCoy, Spaces of densely continuous forms, Set-Valued Anal., 5 (1997), 247–266.
  • James E. Joseph, Multifunctions and graphs, Pacific J. Math., 79(2) (1978), 509–529.
  • M. Matejdes, Sur les sélecteurs des multifonctions, Math. Slovaca, 37 (1987), 111–124.
  • M. Matejdes, Continuity of multifunctions, Real Anal. Exchange, 19(2) (1993-94), 394–413.
  • M. Matejdes, Graph quasi-continuity of the functions, Acta Mathematica, 7 (2004), 29–32.
  • M. Matejdes, Selections theorems and minimal mappings in cluster seeting, (to appear).
  • T. Neubrunn, Quasi-continuity, Real Anal. Exchange, 14(2) (1998/9), 258–307.
  • T. Neubrunn, On quasi-continuity of multifunctions, Math. Slovaca, 32 (1982), 147–154.
  • R. E. Smithson, Subcontinuity for multifunctions, Pacific J. Math., 61 (1975), 283–288.