\begin{definition}[Definition:Coarser Topology/Strictly Coarser]
Let $S$ be a set.
Let $\tau_1$ and $\tau_2$ be topologies on $S$.
Let $\tau_1 \subsetneq \tau_2$.
Then $\tau_1$ is said to be '''strictly coarser''' than $\tau_2$.
This can be expressed as:
:$\tau_1 < \tau_2 := \tau_1 \subsetneq \tau_2$
\end{definition}