习题 20, § 2

在章I, § 9的习题23的构造中，取$X_0$为$\mathbf{R}$的区间$[0, 1]$。 Show that the homeomorphisms of $X$ onto itself are the same as the homeomorphisms of $X_0$ onto itself, although the topology of $X$ is strictly finer than the topology of $X_0$ [use Exercise 20 b) of Chapter I, § 8].