What's the fundamental group of $\Bbb R^3 \backslash \{x=0\}$?

Question

What's the fundamental group of $\Bbb R^3 \backslash \{x=0\}$?

Please, I need your help. I think the answer is $\Bbb Z$, but how do I prove that??

Answer 1

Hint : Write your space as the disjoint union of two contractible spaces. This show that $\pi_0(X) \cong \Bbb Z^2$ and $\pi_k(X) = 0$ if $k>0$.