Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (z-ai/glm-5.2)audited 2026-07-31
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.
Second countability: an at most countable basis for the topology
Definition
A topological space is second countable when its topology has a basis that is at most countable (Basis and subbasis for a topology, and the topology generated by a family of sets, Finite, countably infinite, countable, uncountable). Thus every open set is a union of members of one at most countable family .
Definition references
Remarks
The basis is global. This differs from first countability, where the countable family is allowed to depend on the point.