DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-16

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.

Maps and isomorphisms of covering spaces over a fixed base

Definition

For coverings $p : E \to B$ and $q : F \to B$ , a map of covering spaces over $B$ is a continuous map $h : E \to F$ with $q \circ h = p$ . It is an isomorphism of covering spaces when $h$ is a homeomorphism; its inverse is then also over $B$ (Homeomorphism, open map, closed map, embedding, and what it means for a property to be topological, Covering maps, evenly covered neighbourhoods, fibres, sheets, and trivial coverings).

Depends on

Used by

Deck transformations and the deck-transformation group of a covering Definition

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 23 results over 10 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources

Allen Hatcher, Algebraic Topology, §1.3 (standard reference, not scraped)
J. Peter May, A Concise Course in Algebraic Topology, Ch. 3 (standard reference, not scraped)
Marco Gualtieri, MAT1300 Week 4 Term 2, §1.6 (standard reference, not scraped)