connected component

连通分支

Geometry & Topology · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

A maximal connected subset of a topological space.

拓扑空间中关于包含关系极大的连通子集。

Example

Each singleton is a connected component of Q\mathbb Q.

Usage and distinctions

Components are closed but need not be open; local connectedness makes them open.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 11D, Connected components · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第6周10月17日，主要概念：连通分支 · Checked 2026-10-14
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