  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.
