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  "body": "\n## Summary\n\nA Tychonoff space is a [[T1 space|0NW6CH38YR]] with many continuous real functions.\nEvery point can be separated by such a function from every closed set that does not contain it.\nSuch spaces are exactly the subspaces of products of copies of $[0, 1]$, up to homeomorphism.\nThey are also exactly the spaces that embed in some compact Hausdorff space.\nMetric spaces and compact Hausdorff spaces are Tychonoff.\n\n## Explanations\n\n### L1 human\n\nIn a Tychonoff space, there are enough continuous real functions to describe the topology.\nGiven a point and a closed set away from it, there is a function that is $0$ at the point and $1$ on the set.\nYou can think of such a function as a continuous hill that rises from the point to the set.\nIn the plane, for a point $p$ and a closed set $F$ with $p \\notin F$, the function $\\min(1, d(x, p)/d(p, F))$ does the job.\n",
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