DefinitionDefinition: AI-adaptedProof: 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.

Skeletal mapping telescope of a cw pair

Definition

For a CW pair $(X, A)$ let $X^{i}$ be its $i$ -skeleton and $A^{i} = A \cap X^{i}$ , following Skeleta, CW subcomplexes, and relative CW complexes. Its skeletal mapping telescope is the CW pair $T_{X} = ⋃_{i \geq 0} X^{i} \times [i, \infty), T_{A} = ⋃_{i \geq 0} A^{i} \times [i, \infty) .$ Give $[0, \infty)$ vertices at the nonnegative integers and use the CW weak topology on these subcomplexes of $X \times [0, \infty)$ . Projection $p (x, t) = x$ defines a continuous map $(T_{X}, T_{A}) \to (X, A)$ . The telescope of the empty space is empty.

Depends on

Skeleta, CW subcomplexes, and relative CW complexes

Skeletal mapping telescope of a cw pair

Definition

Depends on

Dependency tree · 2 levels

Sources