null-homotopic map

零伦

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

Other names / variants: null homotopy

Translation evidence: Literature usage

Meaning in context

A continuous map homotopic to a constant map, with any required based or relative condition stated separately.

同伦于常值映射的连续映射；若要求保基点或相对某子集，应另行说明。

Example

A map into Rn\mathbb R^n is null homotopic by linear contraction.

Usage and distinctions

For a loop, contraction in the fundamental group fixes its endpoint basepoint; an unqualified null homotopy of general maps does not.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Allen Hatcher — Algebraic TopologyChapter 0, Homotopy and Homotopy Type, printed pp. 3–4 · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第10周11月14日，主要概念：零伦 · Checked 2026-10-14
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