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  "body": "\n## Summary\n\nA locale is a generalized topological space described only by its lattice of \"open sets\", which is a [[frame|306PWGH7BF]].\nMaps of locales go in the opposite direction to frame homomorphisms, just as a continuous map pulls open sets back.\nEvery topological space gives a locale, and for [[sober spaces|4N4DNDR22Z]] the space can be recovered from it.\nLocales are the objects of [[pointless topology|CYEMGH98WN]].\n\n## Explanations\n\n### L1 human\n\nA continuous map $f \\colon X \\to Y$ sends points forward but sends open sets backward, by taking preimages.\nIf one only remembers the open sets, it is natural to describe a map of spaces by a map of open-set lattices going the other way.\nA locale is a frame regarded in this reversed way, as a space.\nThe real line, for instance, gives the locale whose frame is the set of open subsets of $\\R$.\nThere are also nontrivial locales with no points at all, which have no counterpart among ordinary spaces.\n",
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