Alphabeta MathHow 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 and , a map of covering spaces over is a continuous map with . It is an isomorphism of covering spaces when is a homeomorphism; its inverse is then also over (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
- Based connected coverings are isomorphic exactly when their induced subgroups are equal Corollary
- Deck transformations and the deck-transformation group of a covering Definition
- A based morphism between connected coverings exists exactly when the induced subgroups are included Proposition
- Connected covering spaces are classified by conjugacy classes of fundamental-group subgroups Theorem
Dependency tree · two levels
8 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, §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)