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Covering the Unit Sphere of Certain Banach Spaces by Sequences of Slices and Balls
Published online by Cambridge University Press: 20 November 2018
Abstract
We prove that, given any covering of any infinite-dimensional Hilbert space $H$ by countably many closed balls, some point exists in $H$ which belongs to infinitely many balls. We do that by characterizing isomorphically polyhedral separable Banach spaces as those whose unit sphere admits a point-finite covering by the union of countably many slices of the unit ball.
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- Copyright © Canadian Mathematical Society 2014
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