TITLE: Examples of closed sets with empty interior
QUESTION [16 upvotes]: 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.

REPLY [6 votes]: The fat Cantor set has not only empty interior but positive measure! This shows that having no interior is actually a very weak condition.