习题 18, § 11

令X为实平面$\mathbf{R}^2$，令R为X上的等价关系，其等价类是$\beta > 0$的线$y = \beta$和所有$\alpha \in \mathbf{R}$的半线$x = \alpha, y \leq 0$。 Show that if X/R is regarded as a subset of $\mathfrak{B}_0(X)$, then the topology induced on X/R by $\mathfrak{T}_\Omega$ (§ 2, Exercise 7) is discrete, and that the topology induced on X/R by $\mathfrak{T}_\Phi$ is not discrete but makes X/R into a non-connected space. 最后证明 X/R 与商拓扑相连。*