homotopy

同伦

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

Other names / variants: homotopy of maps

Translation evidence: Literature usage

Meaning in context

A continuous map H from X times the unit interval to Y whose endpoint slices are the specified continuous maps X to Y.

连续映射 $H:X\times[0,1]\to Y$，其两端切片分别为给定的两个连续映射。

Example

For maps into a convex Euclidean set, $H(x,t)=(1-t)f(x)+tg(x)$ is a homotopy.

Usage and distinctions

Continuity must be joint in x and t; based or relative homotopies impose additional fixed-point conditions.

Read the encyclopedia explanation

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Allen Hatcher — Algebraic TopologyChapter 0, Homotopy and Homotopy Type, printed p. 3 · Checked 2026-10-14

Translation sources

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

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