regular covering space

正则复迭空间

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

Other names / variants: normal covering space

Translation evidence: Literature usage

Meaning in context

A covering map for which the deck-transformation group acts transitively on each fiber, so any two points over the same base point are related by a deck transformation.

复迭映射的每根纤维上，复迭变换群的作用均为传递的，即同一底点上方任意两点可由某个复迭变换相连。

Example

For p:S1→S1p:S^1\to S^1, p(z)=znp(z)=z^n with n≥1n\geq1, multiplication by the nth roots of unity gives deck transformations acting transitively on each fiber.

Usage and distinctions

Regularity concerns covering symmetries, not regular topological separation. For path connected coverings over path connected locally path connected bases, it is equivalent to normality of the associated fundamental-group subgroup.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Allen Hatcher — Algebraic Topology§1.3, Deck Transformations and Group Actions, normal/regular covering definition and Proposition 1.39, printed pp. 70–71 · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第15周12月19日，主要概念及特别关注：正则复迭空间 · Checked 2026-10-14
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