Multiplication on uniform $\lambda$-Cantor sets

Jiangwen Gu, Kan Jiang, Lifeng Xi +1

Let $C$ be the middle-third Cantor set. Define $C\ast C=\{x\ast y:x,y\in C\}$, where $\ast =+,-,\cdot ,÷$ (when $\ast =÷$, we assume $y\ne 0$). Steinhaus \cite{HS} proved in 1917 that \[ C-C=[-1,1]…