Complement of Closed Interval with Closed Subset

Question

I have a basic topology question. Let's say I have some interval $[a,b] \subset \mathbb{R}$ and $K \subset [a,b]$, with $K$ closed and having positive measure (this is not entirely relevant). Is it true that $U = [a,b] \setminus K$ is open in the topology on $\mathbb{R}$?

Answer 1

Take for example $[\frac{1}{2},\frac{3}{4}] \subseteq [0,1]$. Now, $[0,1] \setminus [\frac{1}{2},\frac{3}{4}]$ has no open balls around zero contained in the set.