Assouad dimensions of complementary sets. Issue 3 (12th April 2018)

• Record Type: Journal Article
• Authors: García, Ignacio; Hare, Kathryn; Mendivil, Franklin
• Is Part Of: Proceedings. Volume 148:Issue 3(2018)
• Page Start: 517
• Page End: 540
• Publication Date: 2018-04-12
• Subjects: Assouad dimension, -- complementary sets, -- Cantor set; Primary 28A80, -- Secondary 28A78; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210517000488
• Languages: English
• ISSNs: 0308-2105

Abstract

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.