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Uniform Mazur's Intersection Property of Balls
Published online by Cambridge University Press: 20 November 2018
Abstract
We give a dual characterization of the following uniformization of the Mazur's intersection property of balls in a Banach space X: for every ∊ > 0 there is a K > 0 such that whenever a closed convex set C ⊂ X and a point p ∊ X are such that diam C ≤ 1/∊ and dist(p, C) ≤ ∊, then there is a closed ball B of radius ≤ K with B ⊃ C and dist(p,B) ≥ ∊/2.
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- Research Article
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- Copyright © Canadian Mathematical Society 1987
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