Meaning of Heine-Borel theorem

Hei'ne-Bo•rel' the"orem

Pronunciation: (hī'nu-bô-rel', -bu-), [key]
— Math. Math.
  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. Also called
Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease.