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complementary sets

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Assouad dimensions of complementary sets
Part of
- Classical measure theory
Ignacio García, Kathryn Hare, Franklin Mendivil
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 148 / Issue 3 / June 2018

Published online by Cambridge University Press:

12 April 2018, pp. 517-540

Print publication:

June 2018
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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 paper 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.