I've already know that $\{B(x,r):x\in\mathbb{Q}^d,r\in \mathbb{Q}\} $ is an countable base of $\mathbb{R}^d$. Intuitively, I wonder that can an open set $\Omega\subset \mathbb{R}^d$ be countably union of closed balls (.i.e. $\displaystyle \Omega=\bigcup_{n\in\mathbb{N}}B'_n$, where $(B'_n)_n$ are closed balls).
Thanks in advance