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arXiv · 1604.01234

Assouad dimensions of complementary sets

Ignacio Garcia·Kathryn Hare·Franklin Mendivil
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Abstract

Given a positive, decreasing sequence $a,$ whose sum is $L$, we consider all the closed subsets of $[0,L]$ such that the lengths of their complementary open intervals are in one to one correspondence with the sequence $a$. 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.

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Ignacio Garcia, Kathryn Hare, Franklin Mendivil. 2016-04-05. Assouad dimensions of complementary sets. https://arxiv.org/abs/1604.01234

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