DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (deepseek-v4-pro + claude-opus-5[1m])audited 2026-08-24

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.

A solid between continuous graphs over a compact Jordan base

Definition

For a compact Jordan set $D \subseteq R^{m}$ and continuous functions $α, β : D \to R$ with $α \leq β$ , the solid between their graphs is $K = {(u, t) : u \in D, α (u) \leq t \leq β (u)}$ .

The weak inequality is part of the definition. Thus a vertical section may be a singleton, and if $D$ is empty then $K$ is empty. Every point of $K$ is specified by the displayed conditions, so the construction requires no choice of representatives.

Depends on

Used by

Dependency tree · two levels

15 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

Michael E. Taylor, Introduction to Analysis in Several Variables, §3.1 (standard reference, not scraped)