Definition:Finer Topology/Definition 2

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Let $S$ be a set.

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

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

Also see


  • 1966: N. Bourbaki: General Topology: Chapter $I$ Topological Structures: $\S2$ Continuous functions: $2$: Comparison of topologies: Definition 3