This Prove that $\mathbb R ^n $ without a finite number of points is simply connected for $n\geq 3$ shows that $\mathbb R^n$ minus a finite set is simply connected for $n \ge 3$. I know that $\mathbb R^n$ minus a countable set is path connected.
My question is: Is $\mathbb R^n$ minus a countable set simply connected i.e. has trivial fundamental group , for $n \ge 3$ ?