locally connected space

局部连通

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

Translation evidence: Literature usage

Meaning in context

A space in which every open neighborhood of a point contains a connected open neighborhood of that point.

任一点的任意开邻域内都含该点的连通开邻域的空间。

Example

Euclidean balls show Rn\mathbb R^n is locally connected.

Usage and distinctions

Being connected globally does not imply local connectedness, as the topologist's sine curve demonstrates.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 11E, Locally connected spaces · Checked 2026-10-14

Translation sources

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