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  "body": "\n## Definition\n\nA [[topological space|0CNQXVBHCX]] $X$ is Hausdorff when for all points $x \\neq y$ of $X$ there are [[open sets|01ZQQDCERP]] $U$ and $V$ with $x \\in U$, $y \\in V$ and $U \\cap V = \\varnothing$.\n\n## Remarks\n\nEach [[metric space is Hausdorff|0P9DCDES73]]. Subspaces and products of Hausdorff spaces are Hausdorff.\nIn a Hausdorff space, [[limits of sequences are unique|0D8T984XEE]] and [[compact subsets are closed|0MYFJVMN7M]].\nEach Hausdorff space is [[T1|05GQJXBP3F]]. An infinite set with the [[cofinite topology|0B906ZBTMZ]] is T1 but not Hausdorff.\nThe Hausdorff condition is also called T2.\n\n## Explanations\n\n### L1 human\n\nIn a Hausdorff space, you can put any two distinct points into two open sets that do not meet.\nMost spaces of analysis, such as $\\mathbb{R}^n$, are Hausdorff.\n",
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