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.
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.
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019