DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-21

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Regular coverings

Definition

Let $p : E \to B$ be a covering with path-connected total space. It is a regular covering when its deck group acts transitively on every fibre: whenever $e, e^{'} \in E$ satisfy $p (e) = p (e^{'})$ , there is a deck transformation $τ$ with $τ (e) = e^{'}$ (Deck transformations and the deck-transformation group of a covering).

The term normal covering is a synonym. Normality of an induced fundamental-group subgroup is not part of this definition; its equivalence with regularity is proved in A connected covering is regular exactly when its induced subgroup is normal, exactly when deck transformations act transitively on a fibre.

Depends on

Used by

A connected covering is regular exactly when its induced subgroup is normal, exactly when deck transformations act transitively on a fibre Theorem

Dependency tree · two levels

18 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Allen Hatcher, Algebraic Topology, Section 1.3 (standard reference, not scraped)
J. Peter May, A Concise Course in Algebraic Topology, Chapter 3, Section 7 (standard reference, not scraped)