Alphabeta MathHow 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.
Compactly generated based spaces and well-pointed objects
Definition
On this page a based space is a compactly generated weak Hausdorff space equipped with a chosen point . Products are the compactly generated products from the published CGWH convention, and every quotient is kified after taking the ordinary quotient.
A based space is well-pointed when the inclusion
is an unbased cofibration, in the sense of the published homotopy-extension property. Thus well-pointedness is an additional hypothesis: it is not being asserted for every based CGWH space. The structure spaces of every sequential prespectrum on this page are required to be well-pointed. No choice principle is used in these conventions.