Sequentially compact space

In mathematics, a topological space is sequentially compact if every infinite sequence has a convergent subsequence. For general topological spaces, the notions of compactness and sequential compactness are not equivalent; they are, however, equivalent for metric spaces. A metric space X is sequentially compact if every sequence has a convergent subsequence which converges to a point in X.

单词	Sequentially compact space
释义	Sequentially compact space 英语百科 Sequentially compact space In mathematics, a topological space is sequentially compact if every infinite sequence has a convergent subsequence. For general topological spaces, the notions of compactness and sequential compactness are not equivalent; they are, however, equivalent for metric spaces. A metric space X is sequentially compact if every sequence has a convergent subsequence which converges to a point in X.
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