Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T22:16:06.377Z Has data issue: false hasContentIssue false
  • English
  • Français

Three space property for σ-fragmentability

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

Published online by Cambridge University Press:  26 February 2010

Nadezhda K. Ribarska
Nadezhda K. Ribarska
Affiliation:
Sofia University, Department of Mathematics and Informatics, J. Bourchier str. 5, 1126 Sofia, Bulgaria.
Get access

Extract

Let X be a Hausdorff topological space and let ρ be a metric on it, not necessarily related to the topology. The space X is said to be fragmented by the metric ρ if each nonempty set in X has nonempty relatively open subsets of arbitrary small ρ-diameter. This concept was introduced by Jayne and Rogers (see [2]) while they studied the existence of Borel selections for upper semicontinuous set-valued maps.

MSC classification

Secondary: 46B22: Radon-Nikodým, Kreĭn-Milman and related properties
Type
Research Article
Information
Mathematika , Volume 45 , Issue 1 , June 1998 , pp. 113 - 118
Copyright
Copyright © University College London 1998

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.Deville, R., Godefroy, G. and Zizler, V.. Smoothness and renormings in Banach spaces (Longman, U.K., 1993).Google Scholar
2.Jayne, J. E. and Rogers, C. A.. Borel selectors for upper semi-continuous set-valued maps. Acta Math., 56 (1985), 41–79.Google Scholar
3.Jayne, J. E., Namioka, I. and Rogers, C. A.. Topological properties of Banach spaces. Proc. London Math. Soc. (3), 66 (1993), 651–672.CrossRefGoogle Scholar
4.Jayne, J. E., Namioka, I. and Rogers, C. A., σ-fragmentable Banach spaces. Mathematika, 39 (1992), 161–188.Google Scholar
5.Jayne, J. E., Namioka, I. and Rogers, C. A., σ-fragmented Banach spaces II. Studia Math., 111 (1994), 69–80.CrossRefGoogle Scholar
6.Jayne, J. E., Namioka, I. and Rogers, C. A.. Fragmentability and σ-fragmentability. Fund. Math., 143 (1993), 207–220.Google Scholar
7.Jayne, J. E., Namioka, I. and Rogers, C. A.. Norm fragmented weak star compact sets. Collect. Math., 41 (1990), 133–163.Google Scholar
8.Jayne, J. E., Namioka, I. and Rogers, C. A.. Continuous functions on compact totally ordered spaces. J. Fund. Anal., 134 (1995), 261–280.Google Scholar
9.Kenderov, P. S. and Moors, W.. Fragmentability and sigma-fragmentability of Banach spaces. J. London Math Soc., in the press.Google Scholar
10.Molto, A., Orihuela, J. and Troyanski, S.. Locally uniformly rotund renorming and fragmentability. Proc. London Math. Soc., 75 (1997), 619–640.Google Scholar
11.Ribarska, N. K.. Internal characterization of fragmentable spaces. Mathematika, 34 (1987), 243–257.Google Scholar