Heine-Borel theorem in English

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{
  "etymology_text": "Named after the German mathematician Eduard Heine (1821–1881) and the French mathematician Émile Borel (1871–1956).",
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        "A theorem which states that for any subset S of an n-dimensional Euclidean space, S is compact if and only if it is both closed and bounded."
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          "closed",
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        ],
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      "raw_glosses": [
        "(mathematical analysis) A theorem which states that for any subset S of an n-dimensional Euclidean space, S is compact if and only if it is both closed and bounded."
      ],
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        "mathematics",
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      "wikipedia": [
        "Eduard Heine",
        "Heine-Borel theorem",
        "Émile Borel"
      ]
    }
  ],
  "word": "Heine-Borel theorem"
}

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{
  "etymology_text": "Named after the German mathematician Eduard Heine (1821–1881) and the French mathematician Émile Borel (1871–1956).",
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        "A theorem which states that for any subset S of an n-dimensional Euclidean space, S is compact if and only if it is both closed and bounded."
      ],
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        [
          "mathematical analysis",
          "mathematical analysis"
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          "closed",
          "closed set"
        ],
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          "bounded",
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        "(mathematical analysis) A theorem which states that for any subset S of an n-dimensional Euclidean space, S is compact if and only if it is both closed and bounded."
      ],
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        "mathematical-analysis",
        "mathematics",
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      "wikipedia": [
        "Eduard Heine",
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        "Émile Borel"
      ]
    }
  ],
  "word": "Heine-Borel theorem"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2025-02-08 from the enwiktionary dump dated 2025-02-02 using wiktextract (f90d964 and 9dbd323). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

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"Heine-Borel theorem" meaning in English

Proper name