Could I please have an example of closed sets with empty interior? Any topological space. Everything goes.

Remark: This is not homework. I'm in the middle of proving the space of $n$-degree polynomials in $(C[0,1], \lVert \cdot \rVert_\infty)$ is meager. Empty interior of this set (if I'm at all correct...) is the punchline and I just want to understand a bit more the nature of closed sets with empty interior.