{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "063W5JMY85"
    },
    {
      "field": "instance_of",
      "target": "06HE9J7DXF"
    },
    {
      "field": "instance_of",
      "target": "07CJNE6ZAQ"
    },
    {
      "field": "instance_of",
      "target": "0E1MMCAY5B"
    },
    {
      "field": "instance_of",
      "target": "0KXJTZSW9B"
    },
    {
      "field": "instance_of",
      "target": "0NA4FK7B8S"
    },
    {
      "field": "instance_of",
      "target": "0TFDZN6AXP"
    },
    {
      "field": "instance_of",
      "target": "0VTAXQEWQD"
    },
    {
      "field": "instance_of",
      "target": "1WN9B18H86"
    },
    {
      "field": "instance_of",
      "target": "85MM2EA0TK"
    },
    {
      "field": "instance_of",
      "target": "RH1WTN38RQ"
    },
    {
      "field": "specializes",
      "target": "0BY52JW6NK"
    },
    {
      "field": "specializes",
      "target": "0RN765S7DH"
    },
    {
      "field": "specializes",
      "target": "1FAF2VNA4G"
    },
    {
      "field": "specializes",
      "target": "71AWVBG6KH"
    },
    {
      "field": "specializes",
      "target": "A6DPR620B5"
    },
    {
      "field": "specializes",
      "target": "EKXQFD7EMF"
    },
    {
      "field": "specializes",
      "target": "NJQ196M1WR"
    },
    {
      "field": "specializes",
      "target": "P923DHV74J"
    },
    {
      "field": "specializes",
      "target": "VCHJVR9NGH"
    },
    {
      "field": "uses",
      "target": "17BH73YHVT"
    },
    {
      "field": "uses",
      "target": "1DHZ81S0YE"
    },
    {
      "field": "uses",
      "target": "21RJ8035KP"
    },
    {
      "field": "uses",
      "target": "23RK8EZ20P"
    },
    {
      "field": "uses",
      "target": "2H2BRQD0YX"
    },
    {
      "field": "uses",
      "target": "2RCTYXSJ67"
    },
    {
      "field": "uses",
      "target": "4RPGSCQVR9"
    },
    {
      "field": "uses",
      "target": "4SSJ589G6T"
    },
    {
      "field": "uses",
      "target": "4THTYJ07RT"
    },
    {
      "field": "uses",
      "target": "4XGQD57EWF"
    },
    {
      "field": "uses",
      "target": "55V8WAJXXJ"
    },
    {
      "field": "uses",
      "target": "58MWCEYTZD"
    },
    {
      "field": "uses",
      "target": "681NY7506V"
    },
    {
      "field": "uses",
      "target": "6V6WDRHRTF"
    },
    {
      "field": "uses",
      "target": "7QFKD5JXH6"
    },
    {
      "field": "uses",
      "target": "8G4ZKXPV29"
    },
    {
      "field": "uses",
      "target": "8MRPZ4Q4NM"
    },
    {
      "field": "uses",
      "target": "9ZK07AKD4M"
    },
    {
      "field": "uses",
      "target": "A0926EFKVP"
    },
    {
      "field": "uses",
      "target": "CBYB39FTFG"
    },
    {
      "field": "uses",
      "target": "CFRN0G7GDB"
    },
    {
      "field": "uses",
      "target": "D07MBM0S3V"
    },
    {
      "field": "uses",
      "target": "D6FMEQYA76"
    },
    {
      "field": "uses",
      "target": "DQEW4MSD5H"
    },
    {
      "field": "uses",
      "target": "E1B3J3XB1T"
    },
    {
      "field": "uses",
      "target": "E3ECET66DQ"
    },
    {
      "field": "uses",
      "target": "EZ24HDESPB"
    },
    {
      "field": "uses",
      "target": "FCA0J1X07K"
    },
    {
      "field": "uses",
      "target": "FFRM041WQX"
    },
    {
      "field": "uses",
      "target": "FQESQA42JE"
    },
    {
      "field": "uses",
      "target": "GSVBM4F91E"
    },
    {
      "field": "uses",
      "target": "HG4S5HNWXF"
    },
    {
      "field": "uses",
      "target": "HHR8HP3R6G"
    },
    {
      "field": "uses",
      "target": "JPD7Q0P4F6"
    },
    {
      "field": "uses",
      "target": "K5H0RT71A3"
    },
    {
      "field": "uses",
      "target": "KH07KHXJB6"
    },
    {
      "field": "uses",
      "target": "KK0B7V8DCX"
    },
    {
      "field": "uses",
      "target": "KMBHAYAGZ9"
    },
    {
      "field": "uses",
      "target": "KZ00AZ2HFM"
    },
    {
      "field": "uses",
      "target": "M44J4ZJ6Z8"
    },
    {
      "field": "uses",
      "target": "M4HM6A3J54"
    },
    {
      "field": "uses",
      "target": "MHSKT2Z4MX"
    },
    {
      "field": "uses",
      "target": "MV7ADC2DEH"
    },
    {
      "field": "uses",
      "target": "NNAR1HN9BQ"
    },
    {
      "field": "uses",
      "target": "NTK1TVA50A"
    },
    {
      "field": "uses",
      "target": "P6EQTZBBNT"
    },
    {
      "field": "uses",
      "target": "PP3XTZWHNH"
    },
    {
      "field": "uses",
      "target": "PSX7N8WAVB"
    },
    {
      "field": "uses",
      "target": "PYN08Z14ZP"
    },
    {
      "field": "uses",
      "target": "Q2WXAR0PXW"
    },
    {
      "field": "uses",
      "target": "QAAV27WAAP"
    },
    {
      "field": "uses",
      "target": "QSH01NSVXN"
    },
    {
      "field": "uses",
      "target": "RBDJBK63HX"
    },
    {
      "field": "uses",
      "target": "RC22S41ZDB"
    },
    {
      "field": "uses",
      "target": "RTG32790CW"
    },
    {
      "field": "uses",
      "target": "T4EPFGAQ8C"
    },
    {
      "field": "uses",
      "target": "TASMEPWNA6"
    },
    {
      "field": "uses",
      "target": "TS5XH58X86"
    },
    {
      "field": "uses",
      "target": "VT2DVEEVRH"
    },
    {
      "field": "uses",
      "target": "VYP60TA2EC"
    },
    {
      "field": "uses",
      "target": "XA35DT40XS"
    },
    {
      "field": "uses",
      "target": "XDK73D2DEA"
    },
    {
      "field": "uses",
      "target": "XX5MY5CCKX"
    },
    {
      "field": "uses",
      "target": "XY6XAJN7Z7"
    },
    {
      "field": "uses",
      "target": "Y8RZ73N0JA"
    },
    {
      "field": "uses",
      "target": "YB7GN4EAF7"
    },
    {
      "field": "uses",
      "target": "ZCDWXVMDFN"
    },
    {
      "field": "uses",
      "target": "ZFZR65WYBX"
    },
    {
      "field": "about",
      "target": "7QFKD5JXH6"
    },
    {
      "field": "about",
      "target": "KK0B7V8DCX"
    },
    {
      "field": "about",
      "target": "RBDJBK63HX"
    },
    {
      "field": "about",
      "target": "XA35DT40XS"
    }
  ],
  "body": "\n## Summary\n\nA metric space is a set with a distance function between its points.\nThe distance is zero only from a point to itself, it is symmetric, and it satisfies the triangle inequality.\nMetric spaces are the setting for limits, continuity and completeness beyond the real line.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "inventory": [
      "X9NDKZ1MNX"
    ],
    "kind": "concept",
    "msc": [
      "54E35"
    ],
    "name": "Metric space",
    "same_as": {
      "wikidata": "Q180953",
      "wikipedia": "Metric space"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Metric_space"
      }
    ],
    "specializes": [
      "0A3HJX3KTF"
    ],
    "tag": "0VKD1TP7F3"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/0VKD1TP7F3/",
  "links": [
    {
      "field": "specializes",
      "target": "0A3HJX3KTF"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/0VKD1TP7F3.md",
  "msc": [
    "54E35"
  ],
  "name": "Metric space",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0VK/0VKD1TP7F3.md",
  "status": null,
  "tag": "0VKD1TP7F3",
  "uri": "m2://0VKD1TP7F3",
  "url": "https://tamnd.github.io/math2/wiki/metric-space/",
  "writing": {
    "tag": "0VKD1TP7F3",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      }
    ]
  }
}
