Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be a continuous function such that $f\left ( i \right )=0$, for all $i \in \mathbb{Z}$. Which of the following statements is always true ?
- Image $(f)$ is closed in $\mathbb{R}$
- Image $(f)$ is open in $\mathbb{R}$
- $f$ is uniformly continuous
- None of the above.