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  "body": "\n## Summary\n\nTake a set and a family of maps from topological spaces into it.\nThe final topology on the set is the finest topology that makes all these maps continuous.\nThe [[quotient topology|0NQ1H2X495]] and the [[disjoint union topology|ZXJKSB30WF]] are both final topologies.\nA map out of the set is continuous for it exactly when its composites with all the given maps are continuous.\nThe dual notion is the [[initial topology|1NWC3710WW]].\n\n## Explanations\n\n### L1 human\n\nSuppose some spaces you understand map into a set.\nYou want as many open sets as possible while keeping every map continuous.\nSo you declare a set open exactly when each map pulls it back to an open set.\nFor example, the map from $[0, 1]$ onto a circle that glues $0$ to $1$ gives the circle its usual topology this way.\n",
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