Assouad dimensions of complementary sets

作者:Garcia Ignacio; Hare Kathryn*; Mendivil Franklin
来源:Proceedings of the Royal Society of Edinburgh: Section A Mathematics , 2018, 148(3): 517-540.
DOI:10.1017/S0308210517000488

摘要

Given a positive, decreasing sequence a, whose sum is L, we consider alll the closed subsets of [0, L] such that the lengths of their complementary open intervals are in one-to-one correspondence with the sequence .. 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.

  • 出版日期2018-6