Open intervals in sums and products of Cantor sets

Abstract

We give new arguments for sums and products of sufficient numbers of arbitrary central Cantor sets to produce large open intervals. We further discuss the same question for $C^1$ images of such central Cantor sets. This gives another perspective on the results obtained by Astels through a different formulation on the thickness of these Cantor sets. There has been recent interest in the question of products and sums of powers of Cantor sets, and these are addressed by our methods.