On Generalized Continuous Multifunctions and Their Selections
D. K. Ganguly and Piyali Mallick
Source: Real Anal. Exchange Volume 33, Number 2
(2007), 449-456.
Abstract
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.
First Page:
Show
Hide
Keywords: $\mathcal{E}$-cluster point; $\mathcal{E}$-continuity; quasicontinuity; $B$-continuity; Baire continuity; $ B^{*}$-continuity; semi-continuity; subcontinuity; weak-subcontinuity; $\mathcal{E}$-cluster multifunction; densely continuous form
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.rae/1229619422
Mathematical Reviews number (MathSciNet): MR2458261
Zentralblatt MATH identifier: 1160.26001
References
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.
Mathematical Reviews (MathSciNet): MR2218189
Zentralblatt MATH: 1097.54023
Project Euclid: euclid.rae/1149516799
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.
Mathematical Reviews (MathSciNet): MR227952
Zentralblatt MATH: 0165.25304
Project Euclid: euclid.pjm/1102986144
D. K. Ganguly & Chandrani Mitra, On some weaker forms of $B^{*}$ continuity for multifunctions, Soochow J. Math., 32(1) (2006), 59–69.
Mathematical Reviews (MathSciNet): MR2218527
Zentralblatt MATH: 1107.54013
S. T. Hammer & R. A. McCoy, Spaces of densely continuous forms, Set-Valued Anal., 5 (1997), 247–266.
Mathematical Reviews (MathSciNet): MR1486774
Digital Object Identifier: doi:10.1023/A:1008666504767
James E. Joseph, Multifunctions and graphs, Pacific J. Math., 79(2) (1978), 509–529.
Mathematical Reviews (MathSciNet): MR531332
Zentralblatt MATH: 0405.54013
Project Euclid: euclid.pjm/1102805798
M. Matejdes, Sur les sélecteurs des multifonctions, Math. Slovaca, 37 (1987), 111–124.
Mathematical Reviews (MathSciNet): MR899022
M. Matejdes, Continuity of multifunctions, Real Anal. Exchange, 19(2) (1993-94), 394–413.
Mathematical Reviews (MathSciNet): MR1282658
Zentralblatt MATH: 0848.54011
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.
Mathematical Reviews (MathSciNet): MR995972
Zentralblatt MATH: 0679.26003
T. Neubrunn, On quasi-continuity of multifunctions, Math. Slovaca, 32 (1982), 147–154.
Mathematical Reviews (MathSciNet): MR658248
Zentralblatt MATH: 0483.54009
R. E. Smithson, Subcontinuity for multifunctions, Pacific J. Math., 61 (1975), 283–288.
Mathematical Reviews (MathSciNet): MR410656
Zentralblatt MATH: 0317.54022
Project Euclid: euclid.pjm/1102868246
Real Analysis Exchange