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

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

3 Scopus citations

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	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

ASJC Scopus subject areas

Geometry and Topology

Access to Document

10.1007/s12220-013-9400-2

Cite this

@article{2a319c26521e4f2f97c2b1fd808c0a7c,

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",

note = "Publisher Copyright: {\textcopyright} 2013, Mathematica Josephina, Inc.",

year = "2014",

month = oct,

day = "1",

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

language = "English",

volume = "24",

pages = "1891--1897",

journal = "Journal of Geometric Analysis",

issn = "1050-6926",

publisher = "Springer New York",

number = "4",

}

TY - JOUR

T1 - Covering Lp Spaces by Balls

AU - Fonf, Vladimir P.

AU - Levin, Michael

AU - Zanco, Clemente

PY - 2014/10/1

Y1 - 2014/10/1

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

KW - Uniformly rotund spaces

KW - Uniformly smooth spaces

UR - http://www.scopus.com/inward/record.url?scp=84958152812&partnerID=8YFLogxK

U2 - 10.1007/s12220-013-9400-2

DO - 10.1007/s12220-013-9400-2

M3 - Article

AN - SCOPUS:84958152812

SN - 1050-6926

VL - 24

SP - 1891

EP - 1897

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 4

ER -