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Is there an example of a (path-connected) subspace of $\mathbb{R}^3$ which has a nontrivial finite fundamental group? If not, why?

Mizar
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    This has been asked here and on MO before. See http://mathoverflow.net/questions/4478/torsion-in-homology-or-fundamental-group-of-subsets-of-euclidean-3-space and/or http://math.stackexchange.com/questions/155421/torsion-in-homology-groups-of-a-topological-space I don't think we want yet another question on exactly the same subject! – Mariano Suárez-Álvarez May 02 '13 at 21:40
  • Instinctively I would say no. I don't have a formal argument, though... – Daniel Robert-Nicoud May 02 '13 at 21:41
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    See also here for the answer to the same question in $\Bbb R^n$, $n \neq 3$: http://math.stackexchange.com/questions/287009/torsion-on-pi-1x-x-connected-and-open-in-mathbbrn/287018#287018 – Henry T. Horton May 02 '13 at 21:51
  • Thank you all; moreover I've seen that here the open poster explicitly says it's an open problem: http://math.stackexchange.com/questions/36279/the-fundamental-group-of-every-subset-of-mathbbr2-is-torsion-free – Mizar May 03 '13 at 20:32

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