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Does there exist a subspace $X$ of $\mathbb R^2$ or $\mathbb R^3$ such that $\pi_1(X)$(I assume that $X$ is path connected) is finite?

I am just interested in how such space would look like(I have a pretty good intuition from $\mathbb RP^n$ but it would be cool to realy see a space loke that).

I belive the answer is no as I asked my teacher and he said that he never saw such space but I would like to know if there is a defenitive answer.

RT1
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    The $\mathbb{R}^2$ question is here: https://math.stackexchange.com/questions/36279/is-the-fundamental-group-of-every-subset-of-mathbbr2-torsion-free and the $\mathbb{R}^3$ question is partially answered here:https://math.stackexchange.com/questions/3048957/subspaces-of-euclidean-spaces-with-finite-nontrivial-homotopy-groups?rq=1. I'm not sure if this question should be closed as a duplicate or not. – Jason DeVito - on hiatus Oct 05 '22 at 16:18
  • Thanks! I guess I didn't look up the question good enough – RT1 Oct 06 '22 at 16:30

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