Hereditarily Non Uniformly Perfect Sets
Complex Variables
2017-01-24 v2 Dynamical Systems
Geometric Topology
Probability
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.
Keywords
Cite
@article{arxiv.1609.07235,
title = {Hereditarily Non Uniformly Perfect Sets},
author = {Rich Stankewitz and Toshiyuki Sugawa and Hiroki Sumi},
journal= {arXiv preprint arXiv:1609.07235},
year = {2017}
}
Comments
14 pages. See also http://rstankewitz.iweb.bsu.edu/, http://sugawa.cajpn.org/index_E.html, http://www.math.sci.osaka-u.ac.jp/~sumi/