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.
The Hawaiian earring is not a CW complex with its punctured circles as cells
Statement refuted
The Hawaiian earring is a CW complex with the common tangency point as its -cell and each circle minus that point as an open -cell.
Counterexample
Given: The union in of circles of radius tangent at the origin.
Proof technique: direct.
The Hawaiian earring is compact as a closed bounded subset of , and it meets every proposed open -cell (each punctured circle).
This violates A compact subspace of a CW complex meets only finitely many cells, so the proposed cell structure is not a CW complex.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
3 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, Appendix A (standard reference, not scraped)