Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (z-ai/glm-5.2)audited 2026-07-31
How 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.
Uniformizable and separated-uniformizable topological spaces
Definition
A topological space is uniformizable if its topology is induced by some uniformity (The sets containing an entourage ball about each of their points form a topology). It is separated-uniformizable if it is induced by a separated uniformity (Separated uniformity: the intersection of all entourages is the diagonal).