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  "body": "\n## Summary\n\nThe Krull topology is the natural topology on the [[Galois group|0XVR72M51M]] of a Galois extension, possibly of infinite degree.\nA basis of neighbourhoods of the identity is given by the subgroups that fix a finite subextension.\nWith it, the Galois group is a [[profinite group|KA0YDB6QXE]], and [[infinite Galois theory|RVR5QFFD77]] matches intermediate fields with closed subgroups.\n\n## Explanations\n\n### L1 human\n\nTwo symmetries of a large field are declared close when they agree on a big finite piece of the field.\nThe more elements they agree on, the closer they are.\nFor a finite extension, every subgroup is open and the topology carries no new information.\nFor the algebraic closure of $\\Q$, the topology is what makes the group of symmetries behave like a limit of finite groups.\n",
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