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  "body": "\n## Summary\n\nThe compact-open topology is a standard topology on the set $C(X, Y)$ of continuous maps between two topological spaces.\nIts basic open sets ask that the maps send a given compact set into a given open set.\nWhen $Y$ is a metric space, it is the topology of uniform convergence on compact sets.\nIt is the usual topology on mapping spaces in homotopy theory.\n\n## Explanations\n\n### L1 human\n\nTo say that two continuous maps are close, you can look at them on a compact piece of the source.\nThe compact-open topology says a map is near $f$ when it sends each chosen compact piece into an open target region that $f$ also sends it into.\nFor maps from $[0, 1]$ to $\\R$, this is the same as being uniformly close on all of $[0, 1]$.\nFor maps from $\\R$ to $\\R$, it means being uniformly close on each bounded closed interval, but not necessarily on all of $\\R$.\n",
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