Assouad dimensions of complementary sets
Classical Analysis and ODEs
2016-04-06 v1
Abstract
Given a positive, decreasing sequence whose sum is , we consider all the closed subsets of such that the lengths of their complementary open intervals are in one to one correspondence with the sequence . The aim of this note is to investigate the possible values that Assouad-type dimensions can attain for this class of sets. In many cases, the set of attainable values is a closed interval whose endpoints we determine.
Cite
@article{arxiv.1604.01234,
title = {Assouad dimensions of complementary sets},
author = {Ignacio Garcia and Kathryn Hare and Franklin Mendivil},
journal= {arXiv preprint arXiv:1604.01234},
year = {2016}
}