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Mathematics · 术语表

什么是 connected component?

Definition 6.23 University Mathematics — Year 3 · 第 6 章 — General Topology

The connected component of x∈Xx \in X is the union of all connected subsets containing xx — the largest one (Theorem 6.20(3)). Components partition XX and are closed (closures of connected sets are connected). XX is totally disconnected if all components are singletons (Q\Q; the Cantor set of the weekend problem).

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