# Fundamental group of a knot

If the circle and any knot are homeomorphic as topological spaces, why do they have different fundamental groups?

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This seems a good place to note that, for such purposes, a knot $K$ should really be thought of in terms of a pair $(X,K)$, where $X$ is typically $\mathbb{R}^3$ or $S^3$. – Tabes Bridges Oct 13 '12 at 20:49