Heine-Borel theorem

proper noun

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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Meanings

proper noun
  1. mathematical analysisA 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.

Origin

Named after the German mathematician Eduard Heine (1821–1881) and the French mathematician Émile Borel (1871–1956).

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Cite this entry
APA

Heine-Borel theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Heine-Borel%20theorem

MLA

“Heine-Borel theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Heine-Borel%20theorem. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Heine-Borel theorem,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Heine-Borel%20theorem.

Source: Heine-Borel theorem on Wiktionary, CC BY-SA 4.0.