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  "body": "\n## Summary\n\nThe Kuratowski closure axioms are four rules for an operation that sends each subset of a set to a larger subset.\nAn operation that obeys them is a closure operator, and the closure operators on a set correspond exactly to the topologies on that set.\nSo a [[topological space|0CQHFPGJ45]] can be described by its [[closure|0QEAJB91GZ]] operation instead of by its [[open sets|02BH3MCBQB]].\n\n## Explanations\n\n### L1 human\n\nThe closure of a set adds to it all the points that are \"infinitely close\" to it.\nKuratowski picked out four simple rules that this operation always obeys.\nNothing comes from nothing, and a set lies in its closure.\nClosing twice is the same as closing once, and the closure of a union is the union of the closures.\nAny operation with these four rules comes from one and only one topology.\nFor example, on $\\R$ the closure of the open interval $(0, 1)$ is $[0, 1]$, and closing $[0, 1]$ again gives nothing new.\n",
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