topological embedding

嵌入映射

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

Other names / variants: embedding of topological spaces

Translation evidence: Literature usage

Meaning in context

A continuous map that is a homeomorphism onto its image equipped with the subspace topology.

到其像的同胚映射，其中像使用目标空间的子空间拓扑。

Example

The inclusion S1↪R2S^1\hookrightarrow\mathbb R^2 is a topological embedding.

Usage and distinctions

This imposes no differential-rank condition; smooth embeddings additionally require immersion.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 5A, Homeomorphisms, embedding definition · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第2周9月19日，常用例子：嵌入映射 · Checked 2026-10-14
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