Assouad dimensions of complementary sets

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 dimens...

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Bibliographic Details
Published inProceedings of the Royal Society of Edinburgh. Section A. Mathematics Vol. 148; no. 3; pp. 517 - 540
Main Authors García, Ignacio, Hare, Kathryn, Mendivil, Franklin
Format Journal Article
LanguageEnglish
Published Edinburgh, UK Royal Society of Edinburgh Scotland Foundation 01.06.2018
Cambridge University Press
Subjects
Primary 28A80
Cantor set
Assouad dimension
complementary sets
Secondary 28A78
Online AccessGet full text
ISSN0308-2105
1473-7124
1473-7124
DOI10.1017/S0308210517000488

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Summary: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.
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content type line 14
ISSN:0308-2105
1473-7124
1473-7124
DOI:10.1017/S0308210517000488