Assouad dimensions of complementary sets. Issue 3 (12th April 2018) - García, Ignacio; Hare, Kathryn; Mendivil, Franklin
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.