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The relationship between fragmentable spaces and class  spaces
Author(s):
Jian
Yu;
Xian-Zhi
Yuan
Journal:
Proc. Amer. Math. Soc.
124
(1996),
3357-3359.
MSC (1991):
Primary 47H10;
Secondary 46C05
MathSciNet review:
1342049
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Abstract:
In this note, we show that each fragmentable space introduced by Jayne and Rogers in 1985 is of class  which was introduced by Kenderov in 1984. Our example shows that a space which is of class  may not be a fragmentable space.
References:
- 1.
- J. E. Jayne and C. A. Rogers, Borel selectors for upper semicontinuous set-valued maps, Acta Math. 155 (1985), 41-79. MR 87a:28011
- 2.
- P. S. Kenderov, Most of the optimization problems have unique solutions, International Series of Numerical Mathematics, vol. 72, Birkhäuser, Basel, 1984, p. 203-216. MR 88f:90138
- 3.
- R. Engelking, General Topology, 2nd ed., Helderman Verlag, Berlin, 1989. MR 91c:54001
- 4.
- N. K. Ribarska, Internal characterization of fragmentable spaces, Mathematika 34 (1987), 243-257. MR 89e:54063
- 5.
- J. P. R. Christensen, Theorems of Namioka and Johnson type for upper semicontinuous and compact valued set-valued mappings, Proc. Amer. Math. Soc. 86 (1982), 649-655. MR 83k:54014
- 6.
- G. Beer, On a generic optimization problem of P. Kenderov, Nonlinear Analysis, T. M. A. 12 (1988), 647-655. MR 89i:90092
- 7.
- R. W. Hansell, J. E. Jayne and M. Talagrand, First class selectors for weakly upper semicontinuous multivalued maps in Banach spaces, J. Reine Angew. Math. 361 (1985), 201-220. MR 87m:54059a
- 8.
- R. W. Hansell, J. E. Jayne and M. Talagrand, First class selectors for weakly upper semicontinuous multivalued maps in Banach spaces, J. Reine Angew. Math. 362 (1986), 219-220. MR 87m:54059b
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Additional Information:
Jian
Yu
Affiliation:
Institute of Applied Mathematics, Guizhou Institute of Technology, Guiyang, Guizhou, China 550003
Xian-Zhi
Yuan
Affiliation:
Department of Mathematics, The University of Queensland, Brisbane, Queensland 4072, Australia
Address at time of publication:
Department of Mathematics, Statistics & Computer Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5
Email:
xzy@axiom.maths.uq.oz.au, yuan@cs.dal.ca
DOI:
10.1090/S0002-9939-96-03468-5
PII:
S 0002-9939(96)03468-5
Keywords:
Fragmentable space,
class $\mathcal{L}$,
\v Cech-complete space
Received by editor(s):
March 14, 1995
Received by editor(s) in revised form:
April 24, 1995
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1996,
American Mathematical Society
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