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.

Euler characteristic of a finite CW complex

Definition

If $X$ has finitely many cells and $c_{n} (X)$ is its number of $n$ -cells, define $χ (X) = \sum_{n} (- 1)^{n} c_{n} (X)$ . The sum is finite by hypothesis.

Used by

Two CW structures on the circle have the same Euler characteristic Example
Euler characteristic is additive for finite CW pairs Proposition
Euler characteristic of a finite CW product Proposition
Euler–Poincare formula for finite CW complexes Theorem

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

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