simply connected space

单连通

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

Translation evidence: Literature usage

Meaning in context

A nonempty path connected space whose fundamental group at one, hence every, basepoint is trivial.

非空道路连通空间，且任一基点处的基本群为平凡群。

Example

SnS^n is simply connected for n≥2n\geq2.

Usage and distinctions

Trivial fundamental groups on each component do not by themselves imply simple connectivity; path connectedness is required.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Allen Hatcher — Algebraic Topology§1.1, simply-connected definition and Proposition 1.14 · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第11周11月21日，主要概念：单连通 · Checked 2026-10-14
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