"Jordan curve" meaning in English

{
  "etymology_text": "Named after French mathematician Camille Jordan (1838-1922), who first proved the Jordan curve theorem.",
  "forms": [
    {
      "form": "Jordan curves",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Jordan curve (plural Jordan curves)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Curves",
          "orig": "en:Curves",
          "parents": [
            "Shapes",
            "Geometry",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Topology",
          "orig": "en:Topology",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "1950, Joseph Leonard Walsh, The Location of Critical Points of Analytic and Harmonic Functions, American Mathematical Society, page 242:",
          "text": "When μ is small and positive, the locus (1) consists of a Jordan curve near each of the Jordan curves belonging to B.",
          "type": "quote"
        },
        {
          "ref": "1992, Konrad Jacobs, Invitation to Mathematics, page 164:",
          "text": "If fis a closed curve that is one-one on [0,1] except for f(0) = f(I), then we say that f is a Jordan curve. A Jordan curve can be seen as a homeomorphism from the circle C onto a subset of the given space.",
          "type": "quote"
        },
        {
          "ref": "2001, Constantin Carathéodory, Theory of Functions of a Complex Variable, volume 1, page 100:",
          "text": "The most general Jordan curves, like the triangle, have the property of dividing the plane into two regions.",
          "type": "quote"
        }
      ],
      "glosses": [
        "A non-self-intersecting continuous loop in the plane; a simple closed curve."
      ],
      "id": "en-Jordan_curve-en-noun-r5jcO65h",
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "continuous",
          "continuous"
        ],
        [
          "loop",
          "loop"
        ],
        [
          "plane",
          "plane"
        ],
        [
          "simple",
          "simple"
        ],
        [
          "closed",
          "closed"
        ],
        [
          "curve",
          "curve"
        ]
      ],
      "raw_glosses": [
        "(topology) A non-self-intersecting continuous loop in the plane; a simple closed curve."
      ],
      "related": [
        {
          "word": "Jordan arc"
        }
      ],
      "synonyms": [
        {
          "sense": "non-self-intersecting loop in the plane",
          "word": "simple closed curve"
        }
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ],
      "wikipedia": [
        "Camille Jordan",
        "Jordan curve theorem"
      ]
    }
  ],
  "word": "Jordan curve"
}

{
  "etymology_text": "Named after French mathematician Camille Jordan (1838-1922), who first proved the Jordan curve theorem.",
  "forms": [
    {
      "form": "Jordan curves",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Jordan curve (plural Jordan curves)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "Jordan arc"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "Pages with 1 entry",
        "Pages with entries",
        "Quotation templates to be cleaned",
        "en:Curves",
        "en:Topology"
      ],
      "examples": [
        {
          "ref": "1950, Joseph Leonard Walsh, The Location of Critical Points of Analytic and Harmonic Functions, American Mathematical Society, page 242:",
          "text": "When μ is small and positive, the locus (1) consists of a Jordan curve near each of the Jordan curves belonging to B.",
          "type": "quote"
        },
        {
          "ref": "1992, Konrad Jacobs, Invitation to Mathematics, page 164:",
          "text": "If fis a closed curve that is one-one on [0,1] except for f(0) = f(I), then we say that f is a Jordan curve. A Jordan curve can be seen as a homeomorphism from the circle C onto a subset of the given space.",
          "type": "quote"
        },
        {
          "ref": "2001, Constantin Carathéodory, Theory of Functions of a Complex Variable, volume 1, page 100:",
          "text": "The most general Jordan curves, like the triangle, have the property of dividing the plane into two regions.",
          "type": "quote"
        }
      ],
      "glosses": [
        "A non-self-intersecting continuous loop in the plane; a simple closed curve."
      ],
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "continuous",
          "continuous"
        ],
        [
          "loop",
          "loop"
        ],
        [
          "plane",
          "plane"
        ],
        [
          "simple",
          "simple"
        ],
        [
          "closed",
          "closed"
        ],
        [
          "curve",
          "curve"
        ]
      ],
      "raw_glosses": [
        "(topology) A non-self-intersecting continuous loop in the plane; a simple closed curve."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ],
      "wikipedia": [
        "Camille Jordan",
        "Jordan curve theorem"
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "non-self-intersecting loop in the plane",
      "word": "simple closed curve"
    }
  ],
  "word": "Jordan curve"
}