Heine–Borel theorem: Difference between revisions
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Revision as of 06:44, 29 December 2008
In mathematics, the Heine-Borel theorem characterises the compact subsets of the real numbers.
The real numbers form a metric space with the usual distance as metric. As a topological space, a subset is compact if and only if it is closed and bounded.
A Euclidean space of fixed finite dimension n also forms a metric space with the Euclidean distance as metric. As a topological space, the same statement holds: a subset is compact if and only if it is closed and bounded.