universal covering space

泛复迭空间

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

Translation evidence: Literature usage

Meaning in context

A covering with path connected and simply connected total space.

总空间道路连通且单连通的复迭空间。

Example

R→S1\mathbb R\to S^1 is a universal covering.

Usage and distinctions

Existence is guaranteed for path connected, locally path connected, semilocally simply connected bases, not arbitrary spaces.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Allen Hatcher — Algebraic Topology§1.3, Classification of Covering Spaces, universal covering discussion · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第15周12月19日，主要概念：泛复迭空间 · Checked 2026-10-14
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