{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "10P0C0Y5V0"
    },
    {
      "field": "specializes",
      "target": "VK3ZMD1BCP"
    }
  ],
  "body": "\n## Summary\n\nA completely normal space is a topological space in which every subspace is [[normal|0NSR9V8TED]].\nEquivalently, any two separated sets, where neither meets the closure of the other, lie in disjoint open sets.\nNormality is not inherited by subspaces in general, so this is a real strengthening.\nA completely normal $T_1$ space is called a $T_5$ space.\n\n## Explanations\n\n### L1 human\n\nNormal spaces let you pull apart two closed sets that do not meet.\nIn a completely normal space, you can do more: you can pull apart two sets that merely keep away from each other's closures.\nFor example, on the real line, the open intervals $(0, 1)$ and $(1, 2)$ touch at the point $1$, yet neither contains a limit point of the other.\nThey lie in the disjoint open sets $(0, 1)$ and $(1, 2)$.\nEvery metric space is completely normal.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "kind": "concept",
    "msc": [
      "54D15"
    ],
    "name": "Completely normal space",
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Normal_space"
      }
    ],
    "specializes": [
      "0NSR9V8TED"
    ],
    "tag": "9HBDQ2W9CF"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/9HBDQ2W9CF/",
  "links": [
    {
      "field": "specializes",
      "target": "0NSR9V8TED"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/9HBDQ2W9CF.md",
  "msc": [
    "54D15"
  ],
  "name": "Completely normal space",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/9HB/9HBDQ2W9CF.md",
  "status": null,
  "tag": "9HBDQ2W9CF",
  "uri": "m2://9HBDQ2W9CF",
  "url": "https://math2.tamnd.com/wiki/completely-normal-space/",
  "writing": {
    "tag": "9HBDQ2W9CF",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}