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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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