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In mathematics, a subset of Euclidean space R^n is called compact if it is
closed and bounded. For example, in R, the closed unit interval [LINK: 0,]
1 is compact, but the set of integers Z is not (it is not bounded) and
neither is the half-open interval [0, 1) (it is not closed).
A more modern approach is to call a topological space compact if each of
its open covers has a finite subcover. The Heine?Borel theorem shows that
this definition is equivalent to "closed and bounded" for subsets of
Euclidean space.
Note: Some authors such as Bourbaki use the term "quasi-compact" instead,
and reserve the term "compact" for topological spaces that are Hausdorff
and "quasi-compact". A single compact set is sometimes referred to as a
compactum; following the Latin second declension , the corresponding p
