Definition:Finer Topology/Definition 2

Definition
Let $S$ be a set.

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

$\tau_1$ is finer than $\tau_2$ the identity mapping $(S, \tau_1) \to (S, \tau_2)$ is continuous.

Also see

 * Equivalence of Definitions of Finer Topology