contractible space

可缩空间

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

Translation evidence: Literature usage

Meaning in context

A nonempty topological space whose identity map is homotopic to a constant map.

非空拓扑空间，其恒等映射同伦于一个常值映射。

Example

Every nonempty convex subset of $\mathbb R^n$ is contractible.

Usage and distinctions

Contractibility implies trivial positive homotopy and reduced homology, but trivial homology alone does not imply contractibility.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Allen Hatcher — Algebraic TopologyChapter 0, Homotopy and Homotopy Type, printed p. 4 · Checked 2026-10-14

Translation sources

1. Bao Zhiqiang — Peking University topology syllabus第11周11月23日，主要概念：可缩空间 · Checked 2026-10-14

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