{
  "aliases": [
    "complete-normed-space"
  ],
  "backlinks": [
    {
      "field": "instance_of",
      "target": "08P6T2WH6R"
    },
    {
      "field": "instance_of",
      "target": "0KNJWEVSMG"
    },
    {
      "field": "instance_of",
      "target": "0PARCKE8WP"
    },
    {
      "field": "instance_of",
      "target": "2N4RJCW5JK"
    },
    {
      "field": "instance_of",
      "target": "5Z00K7K1HY"
    },
    {
      "field": "instance_of",
      "target": "DYAWGXE2GV"
    },
    {
      "field": "instance_of",
      "target": "G3F2CWQSQH"
    },
    {
      "field": "instance_of",
      "target": "GWCBGYG5RA"
    },
    {
      "field": "instance_of",
      "target": "S49XMZKGQC"
    },
    {
      "field": "instance_of",
      "target": "WDH6QSH1Z6"
    },
    {
      "field": "defines",
      "target": "0BDTTM24DP"
    },
    {
      "field": "uses",
      "target": "17PWP8MB4X"
    },
    {
      "field": "uses",
      "target": "18ZNC2R6AX"
    },
    {
      "field": "uses",
      "target": "1A8A1XFG45"
    },
    {
      "field": "uses",
      "target": "1JNFB7XBDN"
    },
    {
      "field": "uses",
      "target": "1YDR94WQMZ"
    },
    {
      "field": "uses",
      "target": "23DM2PQC78"
    },
    {
      "field": "uses",
      "target": "2MTN8CQWME"
    },
    {
      "field": "uses",
      "target": "2N4RJCW5JK"
    },
    {
      "field": "uses",
      "target": "2RCTYXSJ67"
    },
    {
      "field": "uses",
      "target": "2VQDK71A27"
    },
    {
      "field": "uses",
      "target": "3F94J43P2C"
    },
    {
      "field": "uses",
      "target": "3NFC6F0Z9F"
    },
    {
      "field": "uses",
      "target": "3PGXH0T1K6"
    },
    {
      "field": "uses",
      "target": "3RJ1K36A9A"
    },
    {
      "field": "uses",
      "target": "3SVWD5SN15"
    },
    {
      "field": "uses",
      "target": "3X4YMR25ST"
    },
    {
      "field": "uses",
      "target": "405TSJS5PA"
    },
    {
      "field": "uses",
      "target": "47NSS1R24Y"
    },
    {
      "field": "uses",
      "target": "54BD10ZZDN"
    },
    {
      "field": "uses",
      "target": "7H3YSSDEBK"
    },
    {
      "field": "uses",
      "target": "7KHRRDRVA6"
    },
    {
      "field": "uses",
      "target": "7KMD9JA3QZ"
    },
    {
      "field": "uses",
      "target": "7Q9YSCM8YY"
    },
    {
      "field": "uses",
      "target": "8D5Y3JNF09"
    },
    {
      "field": "uses",
      "target": "8QJ91709V2"
    },
    {
      "field": "uses",
      "target": "8V9J445R7N"
    },
    {
      "field": "uses",
      "target": "93WX6PZC8R"
    },
    {
      "field": "uses",
      "target": "9HNTG5C2XX"
    },
    {
      "field": "uses",
      "target": "ABS17CB1D2"
    },
    {
      "field": "uses",
      "target": "AJ5RG9XQYZ"
    },
    {
      "field": "uses",
      "target": "AR52AWP2XE"
    },
    {
      "field": "uses",
      "target": "ATG4DQZZT9"
    },
    {
      "field": "uses",
      "target": "B538T38WDS"
    },
    {
      "field": "uses",
      "target": "BR6KJEJD1C"
    },
    {
      "field": "uses",
      "target": "BTM6WJ0A52"
    },
    {
      "field": "uses",
      "target": "CC666JT89X"
    },
    {
      "field": "uses",
      "target": "D5M7TRD3MY"
    },
    {
      "field": "uses",
      "target": "DVA7AZ0HDJ"
    },
    {
      "field": "uses",
      "target": "DYAWGXE2GV"
    },
    {
      "field": "uses",
      "target": "E4P30YHWEQ"
    },
    {
      "field": "uses",
      "target": "E7QDFXK2E1"
    },
    {
      "field": "uses",
      "target": "ENB0GT59ZC"
    },
    {
      "field": "uses",
      "target": "EPXNCSP2MN"
    },
    {
      "field": "uses",
      "target": "EYA944RVSY"
    },
    {
      "field": "uses",
      "target": "FH92FW76Q0"
    },
    {
      "field": "uses",
      "target": "G1VWNQSAK5"
    },
    {
      "field": "uses",
      "target": "G4CA22W2XX"
    },
    {
      "field": "uses",
      "target": "GE05N4B84Q"
    },
    {
      "field": "uses",
      "target": "GXM8BX8YM7"
    },
    {
      "field": "uses",
      "target": "H6KS0E9MF5"
    },
    {
      "field": "uses",
      "target": "J9TBJSV9ER"
    },
    {
      "field": "uses",
      "target": "JEBP2FYZFM"
    },
    {
      "field": "uses",
      "target": "JEPDM5B5FC"
    },
    {
      "field": "uses",
      "target": "JKQP7AFZ0E"
    },
    {
      "field": "uses",
      "target": "K768V9ZS7R"
    },
    {
      "field": "uses",
      "target": "K91VB1DXPR"
    },
    {
      "field": "uses",
      "target": "KA3V66S6F5"
    },
    {
      "field": "uses",
      "target": "KD9BP7YJK5"
    },
    {
      "field": "uses",
      "target": "KK0B7V8DCX"
    },
    {
      "field": "uses",
      "target": "KX2XY7S3X6"
    },
    {
      "field": "uses",
      "target": "KZ3YVM10SP"
    },
    {
      "field": "uses",
      "target": "M218MWZ62X"
    },
    {
      "field": "uses",
      "target": "MKB5V9W0WQ"
    },
    {
      "field": "uses",
      "target": "MR5FJXR348"
    },
    {
      "field": "uses",
      "target": "NAJ9Y60PF6"
    },
    {
      "field": "uses",
      "target": "NCWYTR6PH0"
    },
    {
      "field": "uses",
      "target": "NPF2KSXK81"
    },
    {
      "field": "uses",
      "target": "NWK9Z80BT2"
    },
    {
      "field": "uses",
      "target": "NXT0V2QWSC"
    },
    {
      "field": "uses",
      "target": "NYVHMQJP3E"
    },
    {
      "field": "uses",
      "target": "P971S9AX0E"
    },
    {
      "field": "uses",
      "target": "PDVJTYCK8F"
    },
    {
      "field": "uses",
      "target": "PFQJTXX9YG"
    },
    {
      "field": "uses",
      "target": "Q5B5YGY7D6"
    },
    {
      "field": "uses",
      "target": "Q7QK3PF806"
    },
    {
      "field": "uses",
      "target": "QEKVW55VV7"
    },
    {
      "field": "uses",
      "target": "RGWYQCS5A1"
    },
    {
      "field": "uses",
      "target": "S49XMZKGQC"
    },
    {
      "field": "uses",
      "target": "SB04FYJ0A9"
    },
    {
      "field": "uses",
      "target": "T7JBM8472G"
    },
    {
      "field": "uses",
      "target": "TD0N49V1SD"
    },
    {
      "field": "uses",
      "target": "TEREJ8DA37"
    },
    {
      "field": "uses",
      "target": "V60F20N6JT"
    },
    {
      "field": "uses",
      "target": "VADXDK3TKM"
    },
    {
      "field": "uses",
      "target": "VB95VVVDM8"
    },
    {
      "field": "uses",
      "target": "VFRJ0P2P15"
    },
    {
      "field": "uses",
      "target": "VRBP76MM84"
    },
    {
      "field": "uses",
      "target": "W35ZP39S4R"
    },
    {
      "field": "uses",
      "target": "WVV4MFB2SE"
    },
    {
      "field": "uses",
      "target": "XXXSST2DR5"
    },
    {
      "field": "uses",
      "target": "Y0V7AP2E09"
    },
    {
      "field": "uses",
      "target": "YG0042V8CJ"
    },
    {
      "field": "uses",
      "target": "YG46P1T47G"
    },
    {
      "field": "uses",
      "target": "Z2N8MPD8DH"
    },
    {
      "field": "uses",
      "target": "Z4ZM26BJHN"
    },
    {
      "field": "uses",
      "target": "Z5DHRKE2Q0"
    },
    {
      "field": "uses",
      "target": "ZJF5XVY63D"
    },
    {
      "field": "uses",
      "target": "ZKP5KGFWCK"
    },
    {
      "field": "uses",
      "target": "ZRC17G6GYS"
    },
    {
      "field": "uses",
      "target": "ZX8972MACG"
    },
    {
      "field": "about",
      "target": "23DM2PQC78"
    },
    {
      "field": "about",
      "target": "7H3YSSDEBK"
    },
    {
      "field": "about",
      "target": "BTM6WJ0A52"
    },
    {
      "field": "about",
      "target": "KK0B7V8DCX"
    },
    {
      "field": "about",
      "target": "M218MWZ62X"
    },
    {
      "field": "specializes",
      "target": "9YQ999QHHT"
    },
    {
      "field": "specializes",
      "target": "AH45GS6RCR"
    },
    {
      "field": "specializes",
      "target": "F6M8ME0DQR"
    },
    {
      "field": "specializes",
      "target": "HDJ1GKG0NA"
    },
    {
      "field": "specializes",
      "target": "HM2HHE3J51"
    },
    {
      "field": "specializes",
      "target": "MG3X8Y1VT4"
    },
    {
      "field": "specializes",
      "target": "NN8RWPC8WG"
    },
    {
      "field": "specializes",
      "target": "V90RGBV52W"
    }
  ],
  "body": "\n## Summary\n\nA Banach space is a normed vector space that is complete for the metric of its norm.\nBanach spaces are the main setting of functional analysis.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "aliases": [
      "complete-normed-space"
    ],
    "kind": "concept",
    "msc": [
      "46B99"
    ],
    "name": "Banach space",
    "same_as": {
      "wikidata": "Q194397",
      "wikipedia": "Banach space"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Banach_space"
      }
    ],
    "specializes": [
      "03J5RAKB30"
    ],
    "tag": "06GZ956657"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/06GZ956657/",
  "links": [
    {
      "field": "specializes",
      "target": "03J5RAKB30"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/06GZ956657.md",
  "msc": [
    "46B99"
  ],
  "name": "Banach space",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/06G/06GZ956657.md",
  "status": null,
  "tag": "06GZ956657",
  "uri": "m2://06GZ956657",
  "url": "https://tamnd.github.io/math2/wiki/banach-space/",
  "writing": {
    "tag": "06GZ956657",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      }
    ]
  }
}
