Definition:Comparable Topologies

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Definition

Let $S$ be a set.

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


Then $\tau_1$ and $\tau_2$ are comparable iff 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

$\tau_1 \supseteq \tau_2$


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