I need to calculate the fundamental groups of the following spaces:
$X_1 = \{ (x, y, z) \in \mathbb{R}^3 | x \neq 0\} $
$X_2 = \mathbb{R}^3 \backslash \{ (x, y, z) | x = 0, y = 0, 0 \leq z \leq 1 \}$
$X_3 = \mathbb{R}^3 \backslash \{ (x, y, z) | x= 0, 0 \leq y \leq 1 \} $
I'm not sure at all how one would calculate these. I think that $X_1$ is still a convex space, so the fundamental group might be {1} but I'm really not at all sure...I need to calculate the fundamental groups of the following spaces: