{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Definition\n\nA [[topological space|0CNQXVBHCX]] $X$ is T0 when for all $x \\neq y$ in $X$, some [[open set|01ZQQDCERP]] contains exactly one of $x$ and $y$.\n\n## Remarks\n\nEach [[T1 space|05GQJXBP3F]] is T0.\nThe Sierpiński space $\\{0, 1\\}$, with open sets $\\varnothing$, $\\{1\\}$ and $\\{0, 1\\}$, is T0 but not T1.\nAn [[indiscrete space|0XJ02JBD6S]] with at least two points is not T0.\n\n## Explanations\n\n### L1 human\n\nIn a T0 space, no two distinct points have exactly the same open sets around them.\nThe open sets may still fail to separate the points in both directions.\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "defines": "07SG12TQH3",
    "kind": "definition",
    "msc": [
      "54D10"
    ],
    "name": "T0 space",
    "sources": [
      {
        "locator": "Definition",
        "url": "https://en.wikipedia.org/wiki/Kolmogorov_space"
      }
    ],
    "tag": "0R3B7DX55J",
    "uses": [
      "0CNQXVBHCX",
      "01ZQQDCERP"
    ]
  },
  "kind": "definition",
  "link": "https://math2.tamnd.com/node/0R3B7DX55J/",
  "links": [
    {
      "field": "defines",
      "target": "07SG12TQH3"
    },
    {
      "field": "uses",
      "target": "0CNQXVBHCX"
    },
    {
      "field": "uses",
      "target": "01ZQQDCERP"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/0R3B7DX55J.md",
  "msc": [
    "54D10"
  ],
  "name": "T0 space",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0R3/0R3B7DX55J.md",
  "status": null,
  "tag": "0R3B7DX55J",
  "uri": "m2://0R3B7DX55J",
  "url": "https://math2.tamnd.com/wiki/t0-space-definition/",
  "writing": {
    "tag": "0R3B7DX55J",
    "kind": "definition",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "one example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge not_instance_of in",
        "note": "one non-example that fails one clause",
        "have": 0,
        "want": 1
      }
    ]
  }
}