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Covering the Unit Sphere of Certain Banach Spaces by Sequences of Slices and Balls
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- Journal:
- Canadian Mathematical Bulletin / Volume 57 / Issue 1 / 14 March 2014
- Published online by Cambridge University Press:
- 20 November 2018, pp. 42-50
- Print publication:
- 14 March 2014
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- Article
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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.
