Recently I came across the following result :
Let $A \subseteq \mathbb{R}^n$ be a connected set and $f : A \to \mathbb{R}$ a continuous function. If there are two vectors $u$ and $v$ such as $f(u)<0$ and $f(v)>0$ then there exists $w \in A$ such that $f(w)=0$.
Unfortunately the author did not prove this nor did he give any references. How can this be proven provided the fact that there are no constraints on $f$ ?