path component

道路分支

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

Translation evidence: Literature usage

Meaning in context

An equivalence class under the relation that two points can be joined by a path in the space.

按两点之间存在道路这一等价关系得到的等价类。

Example

The topologist's sine curve has a graph path component and a separate vertical-segment path component.

Usage and distinctions

A path component is contained in a connected component, but equality needs additional hypotheses such as local path connectedness.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 12C, Path-connected components · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第7周10月24日，主要概念：道路分支 · Checked 2026-10-14
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