Definition:Compact Space

Topology
A topological space $$X$$ is compact if every open cover of $$X$$ has a finite subcover.

See also the other equivalent definitions of compactness.

For subsets of Euclidean space, this is equivalent to being closed and bounded by the Heine-Borel Theorem.

Real Analysis
A closed real interval is also sometimes described as "compact" through dint of it being closed and bounded.