I'm working through Hatcher book and done $\pi_1(\mathbb{R}^2 - \mathbb{Q}^2)$ is uncountable. It's easy to see that it's true as you can imagine only non trivial maps contract in the space.
But, was wondering has anyone worked out $\pi_2(\mathbb{R}^2 - \mathbb{Q}^2)$. $\pi_2(\mathbb{R}^3 - \mathbb{Q}^3)$ I imagine this isn't that hard, shouldn't it be uncountable aswell.
Just doing a project on higher homotopy theory, but fundamental group stuff seems hard already. Like $\pi_2$ is that just a sphere doing a weird thing and looping back on itself. I know the definition but can't really see it. Plus the calculation aren't that easy.