Continuity of a convex function I'm trying to solve the following problem:
Let $f:K\rightarrow \mathbb{R} $, $f$ convex and $K \subseteq \mathbb{R}^n$ convex. Then $f$ is continuous on $K$. 
I have proved the only case $n=1$, but for an arbitrary $n$??

A hypercube in dimension $n$ has $2n$ hyperfaces, not $2^n$.
Apparently Bacon does not like this to be corrected
(https://math.stackexchange.com/review/suggested-edits/827072).
I do not have enough reputation for a proper comment, I'll delete this as soon as someone put it correctly.
