path-connected space

道路连通

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

Other names / variants: path connectedness

Translation evidence: Literature usage

Meaning in context

A space in which every pair of points is joined by a continuous map from the unit interval.

任意两点都可由从 [0,1][0,1] 出发的连续道路连接的空间。

Example

A convex subset of Rn\mathbb R^n is path connected by straight segments.

Usage and distinctions

Paths may cross themselves and need not be embeddings; path connectedness is stronger than connectedness.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

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

Translation sources

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