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.
Assuming choice, normality is not even finitely productive: two copies of the lower-limit line
Statement refuted
Assuming choice, the product of any finite family of normal spaces is normal.
Facts & Assumptions
Given: The lower-limit-line product theorem.
Under choice, the lower-limit line is normal and its binary square is not normal (Assuming choice, normality is not productive: the normal lower-limit line has a nonnormal square).
Counterexample
Take two copies of the normal lower-limit line from [L1].
Their binary product is not normal by [L1], refuting the claim already for a finite product.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
11 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
- G. Gruenhage, General Topology Course Notes, Sorgenfrey plane (standard reference, not scraped)
- Sorgenfrey plane (Wikipedia) (standard reference, not scraped)