locally path connected space
局部道路连通
Meaning in context
A space in which every open neighborhood of a point contains a path connected open neighborhood of that point.
任一点的每个开邻域内均含该点的道路连通开邻域的空间。
Example
Every topological manifold is locally path connected through its coordinate balls.
Usage and distinctions
On such spaces path components are open and coincide with connected components; global path connectedness alone does not suffice.
Recommended reading in this subject · Preparation & skip guidance
Definition sources
- Anton Petrunin — A minimalist intro to topologyChapter 12D, Locally path-connected spaces · Checked 2026-10-14
Translation sources
- Bao Zhiqiang — Peking University topology syllabus第7周10月24日，主要概念：局部道路连通 · Checked 2026-10-14