{
  "aliases": [
    "continuous-function-of-several-variables",
    "multivariable-continuity"
  ],
  "backlinks": [
    {
      "field": "uses",
      "target": "0C0KPAKK9Y"
    },
    {
      "field": "defines",
      "target": "0S9EK5MQPE"
    }
  ],
  "body": "\n## Summary\n\nTake a function between subsets of Euclidean spaces, and a point $a$. The function is continuous at this point when small changes of the input near $a$ give small changes of the value.\nFor a function of several variables, the input can change in all coordinates at once.\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "aliases": [
      "continuous-function-of-several-variables",
      "multivariable-continuity"
    ],
    "kind": "concept",
    "msc": [
      "26B05"
    ],
    "name": "Continuity in R^n",
    "sources": [
      {
        "locator": "Continuous functions between metric spaces",
        "url": "https://en.wikipedia.org/wiki/Continuous_function"
      }
    ],
    "tag": "0JEJATBVD7",
    "uses": [
      "0J8Y1NCY0K",
      "0XPR1E85W0"
    ]
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/0JEJATBVD7/",
  "links": [
    {
      "field": "uses",
      "target": "0J8Y1NCY0K"
    },
    {
      "field": "uses",
      "target": "0XPR1E85W0"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/0JEJATBVD7.md",
  "msc": [
    "26B05"
  ],
  "name": "Continuity in R^n",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0JE/0JEJATBVD7.md",
  "status": null,
  "tag": "0JEJATBVD7",
  "uri": "m2://0JEJATBVD7",
  "url": "https://math2.tamnd.com/wiki/continuity-in-r-n/",
  "writing": {
    "tag": "0JEJATBVD7",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}