Exercise 2, § 5

Let $A$ be the set of points of $\mathbf{R}^2$ with coordinates $(1/n,0)$, for $n\in \mathbf{N}^*$. Now prove that the fundamental group of $\mathbf{R}^2-$ A has the power of the continuum. It is in particular not isomorphic to the group F(A).