A central set of dimension 2

Christopher J. Bishop; Hrant Hakobyan

doi:10.1090/S0002-9939-08-09173-9

A central set of dimension 2

Christopher J. Bishop
, Hrant Hakobyan

Mathematics

University of Toronto

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

9 Scopus citations

Abstract

The central set of a domain D is the set of centers of maximal discs in D. Fremlin proved that the central set of a planar domain has zero area and asked whether it can have Hausdorff dimension strictly larger than 1. We construct a planar domain with central set of Hausdorff dimension 2.

Original language	English
Pages (from-to)	2453-2461
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	136
Issue number	7
DOIs	https://doi.org/10.1090/S0002-9939-08-09173-9
State	Published - Jul 2008

Keywords

Central set
Disc trees
Hausdorff dimension
Lipschitz domain
Maximal discs
Medial axis
Skeleton

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10.1090/S0002-9939-08-09173-9

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title = "A central set of dimension 2",

abstract = "The central set of a domain D is the set of centers of maximal discs in D. Fremlin proved that the central set of a planar domain has zero area and asked whether it can have Hausdorff dimension strictly larger than 1. We construct a planar domain with central set of Hausdorff dimension 2.",

keywords = "Central set, Disc trees, Hausdorff dimension, Lipschitz domain, Maximal discs, Medial axis, Skeleton",

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AU - Hakobyan, Hrant

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AB - The central set of a domain D is the set of centers of maximal discs in D. Fremlin proved that the central set of a planar domain has zero area and asked whether it can have Hausdorff dimension strictly larger than 1. We construct a planar domain with central set of Hausdorff dimension 2.

KW - Central set

KW - Disc trees

KW - Hausdorff dimension

KW - Lipschitz domain

KW - Maximal discs

KW - Medial axis

KW - Skeleton

UR - https://www.scopus.com/pages/publications/77950838498

U2 - 10.1090/S0002-9939-08-09173-9

DO - 10.1090/S0002-9939-08-09173-9

M3 - Article

AN - SCOPUS:77950838498

SN - 0002-9939

VL - 136

SP - 2453

EP - 2461

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 7

ER -

A central set of dimension 2

Abstract

Keywords

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