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Let $m be two positive integers.

Consider $\mathbb{R}^m$ as a subspace of $\mathbb{R}^n$ via $\mathbb{R}^m\times \{(0,0,...0)\}$.

Any suggestions on how to compute $\pi_1(\mathbb{R}^n\backslash\mathbb{R}^m)$?

I have no idea how to tackle this in the general case, and for the computation of fundamental groups, Van Kampen is the only real method at my disposal so far.

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    Glad to be of assistance! If you complete a proof, you should post it as an answer to your question!2011-10-25

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