DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-07

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.

Compact support of a differential form

Definition

Let $M$ be a smooth manifold, possibly with boundary, and $k \geq 0$ . For $ω \in Ω^{k} (M)$ define $supp ω = {\overline{{p \in M : ω_{p} \neq 0}}}^{M}, Ω_{c}^{k} (M) = {ω \in Ω^{k} (M) : supp ω is compact} .$ The closure and compactness are in $M$ , including its genuine boundary. Zero is the intrinsic zero of each exterior-power fiber, so this definition is independent of trivialization. The zero form has empty support.

Depends on

Used by

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

Merry Definition 26.7, Lecture 26 p.2 / PDF p.214 (standard reference, not scraped)