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Heine-Borel theorem

American  
[hahy-nuh-baw-rel, -buh-] / ˈhaɪ nə bɔˈrɛl, -bə- /

noun

Mathematics.

  1. the theorem that in a metric space every covering consisting of open sets that covers a closed and compact set has a finite collection of subsets that covers the given set.

Etymology

Origin of Heine-Borel theorem

Named after Eduard Heine (1821–81), German mathematician and Émile Borel (1871–1956), French mathematician

Example Sentences

Examples are provided to illustrate real-world usage of words in context. Any opinions expressed do not reflect the views of Dictionary.com.

That comes up in, for example, the proof of the Heine-Borel theorem.

From Scientific American

Definitions and idiom definitions from Dictionary.com Unabridged, based on the Random House Unabridged Dictionary, © Random House, Inc. 2023

Idioms from The American Heritage® Idioms Dictionary copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.