Question 1
What does it mean for one topology on a set $X$ to be finer than another topology on $X$?
Question 2
Which topology on a set $X$ is the coarsest topology on $X$?
Question 3
If two topologies $\tau_1$ and $\tau_2$ on $X$ satisfy $\tau_1 \subseteq \tau_2$, what can be said about them?
Question 4
Which topology on $\mathbb{R}$ is finer: the standard topology or the lower limit topology generated by half-open intervals $[a,b)$?
Question 5
What is the topology generated by a basis $\mathcal{B}$?
