Induced topology

In topology and related areas of mathematics, an induced topology on a topological space is a topology which makes the inducing function continuous from/to this topological space.

Let ${\displaystyle X_{0},X_{1}}$ be sets, ${\displaystyle f:X_{0}\to X_{1}}$.

If ${\displaystyle \tau _{0}}$ is a topology on ${\displaystyle X_{0}}$, then a topology coinduced on ${\displaystyle X_{1}}$ by ${\displaystyle f}$ is ${\displaystyle \{U_{1}\subseteq X_{1}|f^{-1}(U_{1})\in \tau _{0}\}}$.

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