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  "body": "\n## Summary\n\nA perfectly normal space is a [[normal space|0NSR9V8TED]] in which every closed set is a countable intersection of open sets.\nEquivalently, every closed set is the zero set of a continuous real function.\nEvery perfectly normal space is [[completely normal|9HBDQ2W9CF]].\nEvery metric space is perfectly normal.\n\n## Explanations\n\n### L1 human\n\nIn a perfectly normal space, each closed set can be described exactly by one continuous function: the set where the function is zero.\nIn a metric space, the distance to the closed set is such a function.\nFor example, the closed set $[0, 1]$ in $\\R$ is the zero set of the distance $x \\mapsto d(x, [0, 1])$.\nIt is also the intersection of the open sets $(-1/n, 1 + 1/n)$.\n",
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