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.
|Number of pages||12|
|Journal||Discrete and Continuous Dynamical Systems - Series S|
|Publication status||Published - 2019|
- Hausdorff dimension
- Porous sets
- Uniformly perfect sets