So I'm studying for an exam and one of the practice questions is to prove that the complement of R^2 to any countable set A is path connected.(adsbygoogle = window.adsbygoogle || []).push({});

I also assume this extends to any R^n larger than R^2 but that's not important. So this is intuitively obvious, since when you take out these discrete points from R^2 you can always find a path from X to Y anyway (with X and Y being points in R^2 not in A). But how do I go about proving this?

Is there some way to extend the proof that R^n - {0} is path connected? Or is there an easier way? Thank you for your help!

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# R^2 - A, with A being a countable set, path-connected?

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