{
  "aliases": [
    "equivalence-of-norms"
  ],
  "backlinks": [
    {
      "field": "defines",
      "target": "0J3578562S"
    }
  ],
  "body": "\n## Summary\n\nTwo norms on a vector space are equivalent when each is bounded by a constant multiple of the other.\nEquivalent norms give the same open sets, the same convergent sequences and the same Cauchy sequences.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "aliases": [
      "equivalence-of-norms"
    ],
    "inventory": [
      "8DBAMF84XW"
    ],
    "kind": "concept",
    "msc": [
      "46B20"
    ],
    "name": "Equivalent norms",
    "sources": [
      {
        "locator": "Equivalence",
        "url": "https://en.wikipedia.org/wiki/Norm_(mathematics)"
      }
    ],
    "tag": "0M85DXB5RM"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/0M85DXB5RM/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/0M85DXB5RM.md",
  "msc": [
    "46B20"
  ],
  "name": "Equivalent norms",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0M8/0M85DXB5RM.md",
  "status": null,
  "tag": "0M85DXB5RM",
  "uri": "m2://0M85DXB5RM",
  "url": "https://tamnd.github.io/math2/wiki/equivalent-norms/",
  "writing": {
    "tag": "0M85DXB5RM",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}