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.

Skeleta, CW subcomplexes, and relative CW complexes

Definition

Write $X^{n}$ for the union of cells of dimension at most $n$ , with $X^{- 1} = \emptyset$ . A CW subcomplex $A \subseteq X$ is a union of open cells such that, whenever $A$ contains an open cell $e$ , it contains the whole closure $\overline{e}$ . A relative CW complex $(X, A)$ is formed from the subcomplex $A$ by attaching cells in stages; thus $A ↪ X$ is a cellular inclusion.

Skeleta, CW subcomplexes, and relative CW complexes

Definition

Depends on

Dependency tree · 2 levels

Sources