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.

Uniformly continuous map between uniform spaces

Definition

For uniform spaces $(X, U_{X})$ and $(Y, U_{Y})$ , a map $f : X \to Y$ is uniformly continuous if for every $V \in U_{Y}$ there is $U \in U_{X}$ such that $(x, x^{'}) \in U$ implies $(f (x), f (x^{'})) \in V$ . The controlling entourage $U$ is independent of the point $x$ .

Depends on

Uniform space in the entourage formulation

Uniformly continuous map between uniform spaces

Definition

Depends on

Dependency tree · 2 levels

Sources