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A note on porosity and the Mazur intersection property
Author(s) -
Sevilla M. Jiménez,
Moreno J. P.
Publication year - 2000
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300015874
Subject(s) - mathematics , hyperspace , intersection (aeronautics) , banach space , hausdorff space , metric space , property (philosophy) , regular polygon , bounded function , hausdorff distance , pure mathematics , space (punctuation) , combinatorics , discrete mathematics , mathematical analysis , geometry , philosophy , linguistics , epistemology , engineering , aerospace engineering
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.