# Hereditarily non uniformly perfect sets

Rich Stankewitz, Toshiyuki Sugawa, Hiroki Sumi

4 被引用数 (Scopus)

## 抄録

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.

本文言語 English 2391-2402 12 Discrete and Continuous Dynamical Systems - Series S 13 2 https://doi.org/10.3934/dcdss.2019150 Published - 2019

• 分析
• 離散数学と組合せ数学
• 応用数学

## フィンガープリント

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