quotient map

商映射

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

Translation evidence: Literature usage

Meaning in context

A surjective map q of topological spaces such that a subset of the target is open exactly when its inverse image under q is open.

拓扑空间间的满射 qq，满足目标中的子集开当且仅当其原像开。

Example

The endpoint-identification map [0,1]→S1[0,1]\to S^1 is quotient.

Usage and distinctions

A continuous surjection supplies only one direction of the defining equivalence.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 6F, Quotient topology · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第7周10月26日，主要概念：商映射 · Checked 2026-10-14
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