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.
Semilocally simply connected spaces with explicit basepoint convention
Definition
A space is semilocally simply connected at when there is a neighbourhood of and a basepoint-preserving inclusion whose induced map on fundamental groups is trivial (Neighbourhood of a point and neighbourhood base, with this library's convention that a neighbourhood need not be open, The homomorphism on fundamental groups induced by a pointed continuous map, Based loops and the fundamental group). It is semilocally simply connected when this holds at every point. The neighbourhood need not itself be simply connected.
Depends on
Used by
- The based path-class model and basic sets for a universal cover Definition
- The Hawaiian earring is locally path-connected but has no universal cover Example
- For a nonempty path-connected locally path-connected semilocally simply connected space, the path-class projection is a covering map Lemma
- A space admitting a universal covering is semilocally simply connected Theorem
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 32 results over 14 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)