Definition:Compact
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Definition
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 set $X \subset \R$ is said to be compact when it is closed and bounded.
