DefinitionDefinition: 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.

Separated uniformity: the intersection of all entourages is the diagonal

Definition

A uniformity $U$ on $X$ is separated when $⋂_{E \in U} E = Δ_{X}$ (The diagonal $Δ_{X} \subseteq X \times X$ , the diagonal map $δ_{X}$ , and the pairing $⟨ f, g ⟩$ of two maps). Equivalently, whenever $x \neq y$ , some entourage $E$ satisfies $(x, y) \notin E$ . Separation is a property of the uniformity, not an additional convention in the meaning of uniform space.

Depends on

Dependency tree · 2 levels

Sources