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A note on porosity and the Mazur intersection property

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

Published online by Cambridge University Press:  26 February 2010

M. Jiménez Sevilla and
J. P. Moreno
M. Jiménez Sevilla
Affiliation:
Dpto. de Análisis Matemático, Facultad de Ciencias Matematicas, Universidad Complutense de Madrid, Madrid, 28040, Spain. E-mail: marjim@sunaml.mat.ucm.es.
J. P. Moreno
Affiliation:
Dpto. de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, Madrid, 28049, Spain. E-mail: josepedro.moreno@uam.es
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Extract

Let ℳ be the collection of all intersections of balls, considered as a subset of the hyperspace ℳ of all closed, convex and bounded sets of a Banach space, furnished with the Hausdorff metric. It is proved that ℳ is uniformly very porous if and only if the space fails the Mazur intersection property.

MSC classification

Secondary:46B20: Geometry and structure of normed linear spaces

Information

Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000, pp. 267 - 272
Copyright
Copyright © University College London 2000

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