The continuity of additive and convex functions, which are upper bounded on non-flat continua in ${\mathbb{R}}^n$

Taras Banakh, Eliza Jabłońska, Wojciech Jabłoński

We prove that for a continuum $K\subset {\mathbb{R}}^n$ the sum $K^{+n}$ of $n$ copies of $K$ has non-empty interior in ${\mathbb{R}}^n$ if and only if $K$ is not flat in the sense that…