Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-05T08:35:15.237Z Has data issue: false hasContentIssue false
  • English
  • Français

Internal characterization of fragmentable spaces

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  26 February 2010

N. K. Ribarska
N. K. Ribarska
Affiliation:
Institute of Mathematics, Bulgarian Academy of Sciences, 1090 Sofia, P. O. Box 373, Bulgaria.
Get access

Extract

J. E. Jayne and C. A. Rogers in [7] introduced the following notion.

Let X be a topological space and p be a metric defined on X × X. X is said to be fragmented by the metric p if, for every ε > 0 and each nonempty subset Y of X there is a nonempty relatively open subset U of Y such that ρ-diam (U)≤ ε.

MSC classification

Secondary: 46B99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 34 , Issue 2 , December 1987 , pp. 243 - 257
Copyright
Copyright © University College London 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Christensen, H. P. R. and Kenderov, P. S.. Dense strong continuity of mappings and the Radon-Nikodym property. Math. Scand., 54 (1984), 70–78.CrossRefGoogle Scholar
2.Coban, M. M. and Kenderov, P. S.. Generic Gateaux differentiability of convex functionals in C(T) and the topological properties of T. C. R. Acad. Bulgare Sci., 38 (1985), 1603–1604.Google Scholar
3.Čoban, M. M. and Kenderov, P. S.. Generic Gateaux differentiability of convex functionals in C(T) and the topological properties of T. Math, and Education in Math. 1986, Proc. 15-th Conf. Union of Bulg. Mathematicians (Sunny beach, April 1986) 141–149.Google Scholar
4.Debs, G., Espaces K-analytiques et espaces de Baire de fontions continues. Mathematika, 32 (1985), 218–228.CrossRefGoogle Scholar
5.Gruenhage, G.. A note on Gul–ko compact spaces. Proc. Amer. Math. Soc., 100 (1987), 371–376.Google Scholar
6.Hansell, R. W.Jayne, J. E.Talagrand, M.. First class selectors for weakly upper semicontinuous multi-valued maps in Banach spaces. J. fur reine und angew. Math., 361 (1985), 201–220 and 362 (1986), 219-220.Google Scholar
1.Jayne, J. E.Rogers, C. A.. Borel selectors for upper semi-continuous set-valued maps. Acta Math., 155 (1985), 41–79.CrossRefGoogle Scholar
8.Kenderov, P. S.. Multivalued monotone mappings are almost everywhere single-valued. Studia Math., 56 (1976), 199–203.CrossRefGoogle Scholar
9.Kenderov, P. S.. Most of the optimization problems have unique solution. C. R. Acad. Bulgare Sci., 37 (1984).Google Scholar
10.Kenderov, P. S.. C(T) is weak Asplund for every Gul'ko compact T. C. R. Acad. Bulgare Sci., 40 (1987), 17–20.Google Scholar
11.Leiderman, A. G.. Everywhere dense metrizable subspaces of Corson compacta. Mat. Zametki, 38 (1985), 440–449.Google Scholar
12.Namioka, I.. Eberlein and Radon-Naikodym compact spaces. Lecture notes of a course given at University College London, 1985/86. See also Mathematika, 34 (1987), 258–281.CrossRefGoogle Scholar
13.Sokolov, G. A.. On some class of compact spaces lying in Σ-products. Comment. Math. Univ. Carolinae, 25 (1984), 219–231.Google Scholar
14.Stegall, C.. A class of topological spaces and differentiation of functions on Banach spaces, Vorlesungen aus dem Fachbereich Mathematik der Universitat Essen, 1983.Google Scholar
15.Stegall, C.. Topological spaces with dense subspaces that are homeomorphic to complete metric spaces and the classification of C(K) Banach spaces. Mathematika, 34 (1987), 101–107.Google Scholar