Definition:Comparable Topologies

Definition
Let $S$ be a set.

Let $\tau_1$ and $\tau_2$ be topologies on $S$.

Then $\tau_1$ and $\tau_2$ are comparable either:
 * $\tau_1$ is coarser than $\tau_2$

or
 * $\tau_1$ is finer than $\tau_2$

That is, by definition of coarser and finer, either:
 * $\tau_1 \subseteq \tau_2$

or
 * $\tau_1 \supseteq \tau_2$