What is the fundamental group of the complement of the closed disk in $\mathbb R^{3}$ ?
i.e $X = \{(x,y,z)\in \mathbb R^{3} \ | \ z=0, \ x^{2}+y^{2} \leq 1\}$
what is $\pi_{1}(\mathbb R^{3}-X)$ ?
What is the fundamental group of the complement of the closed disk in $\mathbb R^{3}$ ?
i.e $X = \{(x,y,z)\in \mathbb R^{3} \ | \ z=0, \ x^{2}+y^{2} \leq 1\}$
what is $\pi_{1}(\mathbb R^{3}-X)$ ?
This question has been answered in comments. The space is homotopy equivalent to $S^2$, so the fundamental group is trivial.