Hereditarily non uniformly perfect sets

Rich Stankewitz, Toshiyuki Sugawa, Hiroki Sumi

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We introduce the concept of hereditarily non uniformly perfect sets, compact sets for which no compact subset is uniformly perfect, and compare them with the following: Hausdorff dimension zero sets, logarithmic capacity zero sets, Lebesgue 2-dimensional measure zero sets, and porous sets. In particular, we give a detailed construction of a compact set in the plane of Hausdorff dimension 2 (and positive logarithmic capacity) which is hereditarily non uniformly perfect.

Original languageEnglish
Pages (from-to)2391-2402
Number of pages12
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume13
Issue number2
DOIs
Publication statusPublished - 2019 Jan 1

Keywords

  • Capacity
  • Hausdorff dimension
  • Porous sets
  • Uniformly perfect sets

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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