 Formally, a topological space is called "compact" if each of its open covers has a finite subcover.That is, is compact if for every collection of open subsets of such that

there is a finite subset of such that

Some branches of mathematics such as algebraic geometry, typically influenced by the French school of Bourbaki, use the term "quasi-compact" for the general notion, and reserve the term "compact" for topological spaces that are both Hausdorff and "quasi-compact".A compact set is sometimes referred to as a "compactum", plural "compacta".