Relatively compact subspace

（重定向自Relatively bounded）

In mathematics, a relatively compact subspace (or relatively compact subset, or precompact) Y of a topological space X is a subset whose closure is compact.

Since closed subsets of a compact space are compact, every subset of a compact space is relatively compact. In the case of a metric topology, or more generally when sequences may be used to test for compactness, the criterion for relative compactness becomes that any sequence in Y has a subsequence convergent in X.

单词	Relatively bounded
释义	Relatively bounded 英语百科 Relatively compact subspace （重定向自Relatively bounded） In mathematics, a relatively compact subspace (or relatively compact subset, or precompact) Y of a topological space X is a subset whose closure is compact. Since closed subsets of a compact space are compact, every subset of a compact space is relatively compact. In the case of a metric topology, or more generally when sequences may be used to test for compactness, the criterion for relative compactness becomes that any sequence in Y has a subsequence convergent in X.
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