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A topological space is compact if every open cover of the entire space has a finite subcover. For example, [a,b] is compact in R (the Heine-Borel theorem). The continuous image of a compact set is compact, as is a closed subset of a compact set. Moreover, there is a partial converse in that every compact set of a Hausdorff space is closed. The compact subsets of Rⁿ are precisely the closed and bounded subsets. For subsets X ⊆ Rⁿ , X is compact iff it is sequentially compact iff it is closed and bounded. See also totally bounded.