Final topology

In general topology and related areas of mathematics, the final topology (or strong, colimit, coinduced, or inductive topology) on a set ${\displaystyle X}$, with respect to a family of functions into ${\displaystyle X}$, is the finest topology on X which makes those functions continuous.

The dual notion is the initial topology.

Given a set ${\displaystyle X}$ and a family of topological spaces ${\displaystyle Y_{i}}$ with functions

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