homeomorphism

同胚

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

Other names / variants: 同胚映射

Translation evidence: Literature usage

Meaning in context

A bijective continuous map of topological spaces whose inverse is also continuous.

拓扑空间之间的双射，且该映射及其逆映射均连续。

Example

x↦exx\mapsto e^x is a homeomorphism from R\mathbb R to (0,∞)(0,\infty).

Usage and distinctions

Continuity and bijectivity alone do not imply continuity of the inverse.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 5A, Homeomorphisms, printed p. 33 · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第2周9月19日，主要概念：同胚 · Checked 2026-10-14
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