A note on porosity and the Mazur intersection property
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2000
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Cambridge Univ. Press
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Abstract
Let M be the collection of all intersections of balls, considered as a subset of the hyperspace H of all closed, convex and bounded sets of a Banach space, furnished
with the Hausdorff metric. We prove that M is uniformly very porous if and only if the space fails the Mazur intersection property.
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The authors wish to thank the C.E.C.M., the Department of
Mathematics and Statistics of the Simon Fraser University and specially J. Borwein for their hospitality during the preparation of this note. We also thank the referee for valuable suggestions improving its readability