| Let x ∈ (0,1] and the Liiroth expansion of x be defined as where σn (x)≥2 for all n≥1. In this dissertation,we study the sum of Cantor sets from Liiroth expansion, with giving particular attention to the question of when the sum of L(N) form an interval. A analogous question arising from continued fraction expansions, another similar iterated function system, was first settled by Hall[21] in 1947. The main tool of our study is a fundamental theorem of Astels[1] about when the sum of Cantor sets is an interval. |
