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  "body": "\n## Summary\n\nThe topology of pointwise convergence lives on a set of functions from a set $X$ to a space $Y$.\nIn it, convergence means [[pointwise convergence|0GFGK40582]].\nIt is the [[product topology|0GBG8B49AA]] on $Y^X$, or its restriction to a subset such as the continuous maps.\nIt is coarser than the [[topology of uniform convergence|YW5P7NEKR4]] and than the [[compact-open topology|RG15F0TWPW]].\n\n## Explanations\n\n### L1 human\n\nThink of a function $f \\colon X \\to Y$ as a long list of values, one value for each point $x$.\nTwo functions are close in this topology when they are close at finitely many chosen points.\nNothing is asked at the other points.\nFor example, the functions $f_n(x) = x^n$ on $[0, 1]$ converge in this topology to the function that is $0$ on $[0, 1)$ and $1$ at $x = 1$.\nThey do not converge uniformly.\n",
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