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  "body": "\n## Definition\n\nA [[topological space|0CNQXVBHCX]] $X$ is regular when the property that follows holds.\nFor each [[closed set|0G5AV9Q4RR]] $F \\subseteq X$ and each point $x \\in X \\setminus F$, there are [[open sets|01ZQQDCERP]] $U$ and $V$ with $x \\in U$, $F \\subseteq V$ and $U \\cap V = \\varnothing$.\n\n## Remarks\n\nNames vary. Some authors call a space T3 when it is regular and T0, and then it is also [[Hausdorff|0MXB4CKHFW]]. Other authors include this condition in the word regular.\nEquivalently, $X$ is regular if and only if each neighbourhood of a point $x$ contains a closed neighbourhood of $x$.\nEach metric space is regular. Each [[normal|0AJ646N339]] T1 space is regular.\n\n## Explanations\n\n### L1 human\n\nIn a regular space, you can separate a point from a closed set that does not contain it, by two disjoint open sets.\nHausdorff spaces only separate points from points.\n",
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