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.
Universal covering spaces
Definition
A universal covering space of is a covering map whose total space is simply connected (Covering maps, evenly covered neighbourhoods, fibres, sheets, and trivial coverings, Simply connected topological spaces).
Depends on
Used by
- ℝ→ℝ/ℤ is a universal covering Corollary
- Based cellular chains of a universal cover as finite free right group-ring modules Definition
- Right action on universal-cover chains Definition
- A space admitting a universal covering is semilocally simply connected Theorem
- Every nonempty path-connected locally path-connected semilocally simply connected space has a universal cover Theorem
- For a path-connected locally path-connected base, a universal cover maps uniquely over the base to every connected covering, and any two universal covers are uniquely isomorphic 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)