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  "body": "\n## Summary\n\nA Hausdorff topological group is a [[topological group|92700QAB5Y]] whose topology is [[Hausdorff|0S1FJ8VEX9]].\nFor topological groups this is a mild condition: it holds as soon as the one-point set of the identity is closed.\nMany authors include it in the definition of a topological group.\nEvery topological group has a largest Hausdorff quotient, obtained by dividing by the closure of the identity.\n\n## Explanations\n\n### L1 human\n\nIn a Hausdorff space two different points can be put in two disjoint open sets.\nFor a topological group, this follows already from a much weaker looking condition: the identity alone forms a closed set.\nThe real line under addition and every matrix group are Hausdorff.\nA group with the indiscrete topology, where the only open sets are the empty set and the whole group, is not Hausdorff once it has two elements.\n",
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  "name": "Hausdorff topological group",
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