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