How to enclose a ball more than once with a surface homeomorphic to $S^2$? In 3D.

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In 3 dimensional space, how to enclose a monopole (either point-like or ball-like, both types exist.) more than once with a surface homeomorphic to $S^2$?

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If $M$ is a three-manifold and $B$ is a (smoothly embedded, tame) three-ball in $M$, then just take level surfaces of the distance function from $B$. That is, take the surfaces $$S_\epsilon = \{p\in M\ |\ d(p,B) = \epsilon\}.$$

For small $\epsilon$, all $S_\epsilon$ will be diffeomorphic to $\partial B = S^2$.