# 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 if and only if 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

$\tau_1 \supseteq \tau_2$