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arXiv · 1609.07235

Hereditarily Non Uniformly Perfect Sets

Rich Stankewitz·Toshiyuki Sugawa·Hiroki Sumi
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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 an example of a compact set in the plane of Hausdorff dimension 2 (and positive logarithmic capacity) which is hereditarily non uniformly perfect.

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Rich Stankewitz, Toshiyuki Sugawa, Hiroki Sumi. 2016-09-23. Hereditarily Non Uniformly Perfect Sets. https://arxiv.org/abs/1609.07235

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