I am studying Geometrical Theory of Foliations, more specifically: the Complete Stability Theorem, which says: If $\text{Cod}(\mathscr{F}) = 1$, $M$ is an compact and connected manifold, and there is a compact leaf with finite fundamental group, so all the leaves are compact and have finite fundamental group.
Where $\mathscr{F}$ is an foliation on $M$. I am trying to show, by way of an example, that this theorem is not valid in : $\mathbb{R}^{3} - \lbrace 0 \rbrace$.
Any suggestions will be welcome. Thank you very much.
For an example in $\mathbb R^3 - \{0\}$, which is diffeomorphic to $\mathbb S^3 - $(two points), just take a foliation in $S^3$ with compact leaves such as the Hopf foliation, and remove the two points.