Exercise 5, § 1

Let A be the closure in $\mathbf{R}$ of the set of real numbers of the form $1/n$, where $n$ runs through the set of integers $\geqslant$ 1. Let $i$ be the canonical injection of A into $\mathbf{R}$. The canonical mapping of Cone$(i)$ onto $\mathbf{R}/A$ is not a homeotopy.