Covering the unit sphere of certain banach spaces by sequences of slices and balls

Vladimir P. Fonf; Clemente Zanco

doi:10.4153/CMB-2012-027-7

Covering the unit sphere of certain banach spaces by sequences of slices and balls

Vladimir P. Fonf, Clemente Zanco

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English
Pages (from-to)	42-50
Number of pages	9
Journal	Canadian Mathematical Bulletin
Volume	57
Issue number	1
DOIs	https://doi.org/10.4153/CMB-2012-027-7
State	Published - 1 Mar 2014

Keywords

Hilbert spaces
Point finite coverings
Polyhedral spaces
Slices

ASJC Scopus subject areas

General Mathematics

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Cite this

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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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AU - Zanco, Clemente

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N2 - 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.

AB - 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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KW - Polyhedral spaces

KW - Slices

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Covering the unit sphere of certain banach spaces by sequences of slices and balls

Abstract

Keywords

ASJC Scopus subject areas

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