Covering Lp Spaces by Balls

Vladimir P. Fonf; Michael Levin; Clemente Zanco

doi:10.1007/s12220-013-9400-2

Covering L^p Spaces by Balls

Vladimir P. Fonf, Michael Levin, Clemente Zanco

Department of Mathematics

Ben-Gurion University of the Negev

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

Abstract

We prove that, given any covering of any separable infinite-dimensional uniformly rotund and uniformly smooth Banach space X by closed balls each of positive radius, some point exists in X which belongs to infinitely many balls.

Original language	American English
Pages (from-to)	1891-1897
Number of pages	7
Journal	Journal of Geometric Analysis
Volume	24
Issue number	4
DOIs	https://doi.org/10.1007/s12220-013-9400-2
State	Published - 1 Oct 2014

Keywords

Point finite coverings
Slices
Uniformly rotund spaces
Uniformly smooth spaces

All Science Journal Classification (ASJC) codes

Geometry and Topology

Access to Document

10.1007/s12220-013-9400-2

Cite this

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title = "Covering Lp Spaces by Balls",

abstract = "We prove that, given any covering of any separable infinite-dimensional uniformly rotund and uniformly smooth Banach space X by closed balls each of positive radius, some point exists in X which belongs to infinitely many balls.",

keywords = "Point finite coverings, Slices, Uniformly rotund spaces, Uniformly smooth spaces",

author = "Fonf, \{Vladimir P.\} and Michael Levin and Clemente Zanco",

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year = "2014",

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doi = "10.1007/s12220-013-9400-2",

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AU - Levin, Michael

AU - Zanco, Clemente

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N2 - We prove that, given any covering of any separable infinite-dimensional uniformly rotund and uniformly smooth Banach space X by closed balls each of positive radius, some point exists in X which belongs to infinitely many balls.

AB - We prove that, given any covering of any separable infinite-dimensional uniformly rotund and uniformly smooth Banach space X by closed balls each of positive radius, some point exists in X which belongs to infinitely many balls.

KW - Point finite coverings

KW - Slices

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KW - Uniformly smooth spaces

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