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[itex] X_1 = \{ (x,y,z) \in \mathbb{R}^3 | x>0 \}[/itex]

[itex] X_2 = \{ (x,y,z) \in \mathbb{R}^3 | x \neq 0 \}[/itex]

[itex] X_3 = \{ (x,y,z) \in \mathbb{R}^3 | (x,y,z) \neq (0,0,0) \}[/itex]

[itex] X_4 = \mathbb{R}^3 \backslash \{ (x,y,z) \in \mathbb{R}^3 | x=0,y=0, 0 \leqslant z \leqslant 1 \} [/itex]

[itex] X_5 = \mathbb{R}^3 \backslash \{ (x,y,z) \in \mathbb{R}^3 | x=0, 0 \leqslant y \leqslant 1 \} [/itex]

I fundamentally do not understand what a fundamental group is of how to calculate it. I have read the notes on this but they are so so abstract.