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.

Cellular boundary from three consecutive skeleta

Definition

For $n \geq 1$ , define $d_{n} : C_{n}^{c e l l} (X; G) \to C_{n - 1}^{c e l l} (X; G)$ as the connecting map $H_{n} (X^{n}, X^{n - 1}; G) \to H_{n - 1} (X^{n - 1}; G)$ from Long exact sequence of a pair, followed by the quotient map to $H_{n - 1} (X^{n - 1}, X^{n - 2}; G)$ . Set $d_{0} = 0$ .

Depends on

Used by

Dependency tree · two levels

5 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

Allen Hatcher, Algebraic Topology, Section 2.2 (standard reference, not scraped)