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