# Heine-Borel theorem

[hahy-nuh-baw-rel, -buh-]

- 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.

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## Origin of Heine-Borel theorem^{}

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

Also called Borel-Lebesque theorem.

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Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018