deformation retract

强形变收缩

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

Other names / variants: strong deformation retract

Translation evidence: Literature usage

Meaning in context

A subspace A of X for which a homotopy of the identity of X to a retraction onto A fixes every point of A at every time.

子空间 $A\subseteq X$，存在从 $X$ 的恒等映射到映向 $A$ 的收缩映射的同伦，且全程固定 $A$ 中每一点。

Example

The punctured plane strongly deformation retracts onto $S^1$ by radial motion.

Usage and distinctions

Some authors use deformation retract without the fixed-subspace requirement; this record uses the strong convention.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Allen Hatcher — Algebraic TopologyChapter 0, deformation retraction definition, printed p. 2 · Checked 2026-10-14

Translation sources

1. Bao Zhiqiang — Peking University topology syllabus第11周11月23日，主要概念：形变收缩，强形变收缩 · Checked 2026-10-14

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