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  "body": "\n## Summary\n\nAn Urysohn space is a topological space in which any two distinct points have disjoint closed neighbourhoods.\nThis separation axiom, also written $T_{2\\frac12}$, lies between [[Hausdorff|0S1FJ8VEX9]] and regular Hausdorff.\nEvery Urysohn space is Hausdorff, and every regular Hausdorff space is Urysohn.\nSome authors use the name for the stronger notion of a completely Hausdorff space.\n\n## Explanations\n\n### L1 human\n\nIn a Hausdorff space, two points can be put in two open sets that do not meet.\nAn Urysohn space asks a little more: the closures of these open sets must not meet either.\nSo there is a real gap between the two points, not just a thin border.\nEvery metric space is an Urysohn space.\nFor points $x \\ne y$ at distance $r$, the closed balls of radius $r / 3$ around them are disjoint neighbourhoods.\n",
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