Let $S^{1}= \left \{ z \in \mathbb{C} :\left | z \right | =1\right \}$ be the unit circle. Which of the following is false ? Any continuous function from $S^{1}$ to $\mathbb{R}$
- is bounded
- is uniformly continuous
- has image containing a non-empty open subset of $\mathbb{R}$
- has a point $z \in S^{1}$ such that $f\left ( z \right )=f\left ( -z \right )$.
