Interior of certain sums and continuous images of very thin Cantor sets

Yeonwook Jung, Chun-Kit Lai

We show that for all Cantor set $K_1$ on ${\mathbb{R}}^d$, it is always possible to find another Cantor set $K_2$ so that the sum $g(K_1)+K_2$ (where $g$ is a $C^1$ local diffeomor…