Exercise 2, § 6

Let $f: ]0,1]\rightarrow \mathbf{C}$ be the continuous mapping $t\mapsto e^{2\pi i/t}$, let S be its graph. We put X = S.

(a) Prove that the intersection of any two connected open subsets of X is connected.

(b) Prove that the space X is not simply connected (cf. prop. 5 of I, p. 126).