TITLE: What's the fundamental group of $E^2\setminus Q^2$
QUESTION [2 upvotes]: Here $E^2$ is the two-dimensional Euclid space and $Q$ is the set of all rational numbers. Regard $E^2\setminus Q^2$ as a subspace of $E^2$. So what's its fundamental group and how to represent it? I suppose that it's not a free group. Thanks a lot for your help.

REPLY [2 votes]: This has been discussed quite a bit here and here.
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