Hereditarily non uniformly perfect sets

Rich Stankewitz, Toshiyuki Sugawa, Hiroki Sumi

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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
Issue number2
Publication statusPublished - 2019


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


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