Does there exist a function $f:\mathbb{R}\rightarrow\mathbb{R}$ satisfying the following?
- $f$ is unbounded above on every open interval.
- For every $x$, there exists an open interval $S$ containing $x$ such that for all $u\in S$, $f(x)\leq f(u)$.
Does there exist a function $f:\mathbb{R}\rightarrow\mathbb{R}$ satisfying the following?