Sharp Finiteness Principles For Lipschitz Selections

Charles Fefferman; Pavel Shvartsman

doi:10.1007/s00039-018-0467-6

Sharp Finiteness Principles For Lipschitz Selections

Charles Fefferman, Pavel Shvartsman

Mathematics

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

11 Scopus citations

Abstract

Let (M, ρ) be a metric space and let Y be a Banach space. Given a positive integer m, let F be a set-valued mapping from M into the family of all compact convex subsets of Y of dimension at most m. In this paper we prove a finiteness principle for the existence of a Lipschitz selection of F with the sharp value of the finiteness constant.

Original language	English (US)
Pages (from-to)	1641-1705
Number of pages	65
Journal	Geometric and Functional Analysis
Volume	28
Issue number	6
DOIs	https://doi.org/10.1007/s00039-018-0467-6
State	Published - Dec 1 2018

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

Keywords

Helly’s theorem
Lipschitz selection
Metric tree
Nagata dimension
Set-valued mapping
Steiner-type point
Whitney partition

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10.1007/s00039-018-0467-6

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abstract = "Let (M, ρ) be a metric space and let Y be a Banach space. Given a positive integer m, let F be a set-valued mapping from M into the family of all compact convex subsets of Y of dimension at most m. In this paper we prove a finiteness principle for the existence of a Lipschitz selection of F with the sharp value of the finiteness constant.",

keywords = "Helly{\textquoteright}s theorem, Lipschitz selection, Metric tree, Nagata dimension, Set-valued mapping, Steiner-type point, Whitney partition",

author = "Charles Fefferman and Pavel Shvartsman",

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AU - Fefferman, Charles

AU - Shvartsman, Pavel

PY - 2018/12/1

Y1 - 2018/12/1

N2 - Let (M, ρ) be a metric space and let Y be a Banach space. Given a positive integer m, let F be a set-valued mapping from M into the family of all compact convex subsets of Y of dimension at most m. In this paper we prove a finiteness principle for the existence of a Lipschitz selection of F with the sharp value of the finiteness constant.

AB - Let (M, ρ) be a metric space and let Y be a Banach space. Given a positive integer m, let F be a set-valued mapping from M into the family of all compact convex subsets of Y of dimension at most m. In this paper we prove a finiteness principle for the existence of a Lipschitz selection of F with the sharp value of the finiteness constant.

KW - Helly’s theorem

KW - Lipschitz selection

KW - Metric tree

KW - Nagata dimension

KW - Set-valued mapping

KW - Steiner-type point

KW - Whitney partition

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EP - 1705

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 6

ER -

Sharp Finiteness Principles For Lipschitz Selections

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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