I am working on the following problem: for what cardinalities (of $Y$) can $\mathbb{R}^2 - Y$ be a topological group if $Y$ must be finite? My intuition is telling me this somehow involves considering a wedge of circles, but I am not 100% sure on the details. Would anyone be able to confirm this, and if I am wrong, to put me on the right track? Thanks.
2026-04-03 20:56:05.1775249765
For what finite cardinalities of $Y$ is $\mathbb{R}^2 - Y$ a topological group?
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Hint: The fundamental group of a topological group is abelian
The question in the body of the question is different from the title though do you want $\mathbf R^3$ or $\mathbf R^2$.