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σ-fragmentability and analyticity

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

Published online by Cambridge University Press:  26 February 2010

I. Namioka  and
R. Pol
I. Namioka
Affiliation:
Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195-4350, U.S.A.
R. Pol
Affiliation:
Wydzial Mathematyki, Universytet Warszawski, Banacha 2, 02-097 Warszawa 59, Poland.
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Abstract

We present a new characterization of σ-fragmentability and illustrate its usefulness by proving some results relating analyticity and crfragmentability. We show, for instance, that a Banach space with the weak topology is σ-fragmented if, and only if, it is almost Čech-analytic and that an almost Čech-analytic topological space is σ-fragmented by a lower-semicontinuous metric if, and only if, each compact subset of the space is fragmented by the metric.

MSC classification

Secondary: 46B26: Nonseparable Banach spaces
Type
Research Article
Information
Mathematika , Volume 43 , Issue 1 , June 1996 , pp. 172 - 181
Copyright
Copyright © University College London 1996

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References

AL.Aarts, J. M. and Lutzer, D.. Completeness properties designed for recognizing Baire spaces. Dissertationes Math., 116 (1974), 1–48.Google Scholar
Fre.Fremlin, D. H.. Čech-analytic spaces. Note of 8 December, 1980 (Unpublished).Google Scholar
Fro.Frolik, Z.. Generalization of the Gσ-property of complete metric spaces. Czech. Math. J., 10 (1960), 359–379.CrossRefGoogle Scholar
Ha1.Hansell, R. W.. Descriptive sets and the topology of non-separable Banach spaces (1989). Preprint.Google Scholar
Ha2.Hansell, R. W.. Compact perfect sets in weak analytic spaces. Topology and its Applications, 41 (1991), 65–72.CrossRefGoogle Scholar
Ha3.Hansell, R. W.. Descriptive topology. In Recent Progress in General Topology, edited by Hušek, M. and Van Mill, J. (Elsevier Science Publishers, 1992), 275–315.Google Scholar
Ho.Holick, P.ý. Čech-analytic and almost K-descriptive spaces. Čzech. Math. J., 43 (1993), 451–466.CrossRefGoogle Scholar
JR.Jayne, J. E. and Rogers, C. A.. Borel selectors for upper semicontinuous set-valued maps. Acta Math., 155 (1985), 41–79.CrossRefGoogle Scholar
JNR1.Jayne, J. E., Namioka, I. and Rogers, C. A.. Topological properties of Banach spaces. Proc. London Math. Soc, 66 (1993), 651–672.CrossRefGoogle Scholar
JNR2.Jayne, J. E., Namioka, I. and Rogers, C. A., σ-fragmentable Banach spaces. Mathematika, 39 (1992), 161–188 and 197-215.CrossRefGoogle Scholar
Ku.Kuratowski, K.. Topology I (Academic Press, New York-London and PWN-Polish Scientific Publishers, Warsaw, 1966).Google Scholar
Mi1.Michael, E. A.. A note on completely metrizable spaces. Proc. Amer. Math. Soc, 96 (1986), 513–522.CrossRefGoogle Scholar
Mi2Michael, E. A.. Almost complete spaces, hypercomplete spaces, and related mapping theorems. Topology and its Applications, 41 (1991), 113–130.CrossRefGoogle Scholar
My.Mycielski, J.. Independent sets in topological algebras. Fund. Math., 55 (1964), 139–147.CrossRefGoogle Scholar
N.Namioka, I.. Separate continuity and joint continuity. Pacific J. Math., 51 (1974), 515–531.CrossRefGoogle Scholar
StR.Saint Raymond, J.. Jeux topologiques et espaces de Namioka. Proc. Amer. Math. Soc, 87 (1983), 499–504.CrossRefGoogle Scholar
TW.Telgársky, R. and Wicke, H. H.. Complete exhaustive sieves and games. Proc. Amer. Math. Soc, 109 (1987), 737–744.Google Scholar