Assouad dimensions of complementary sets
Published online by Cambridge University Press: 12 April 2018
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 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.
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 3 , June 2018 , pp. 517 - 540
- Copyright
- Copyright © Royal Society of Edinburgh 2018
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