A space is sequentially compact when every sequence has a convergent subsequence. A metric space is compact exactly when it is sequentially compact.
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In topology, a **sequentially compact space** is a type of topological space that extends the concept of compactness in the context of sequences. A topological space \( X \) is said to be **sequentially compact** if every sequence of points in \( X \) has a subsequence that converges to a limit point in \( X \).