DefinitionDefinition: 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.

Separability: the existence of an at most countable dense subset

Definition

A topological space $X$ is separable if some at most countable subset $D \subseteq X$ is dense in $X$ (Dense, nowhere dense and codense subsets of a topological space, and the criterion by basic open sets, Finite, countably infinite, countable, uncountable). Equivalently, every nonempty open subset of $X$ meets $D$ .

Definition references

Dense, nowhere dense and codense subsets of a topological space, and the criterion by basic open sets

Finite, countably infinite, countable, uncountable

Separability: the existence of an at most countable dense subset

Definition

Definition references

Depends on

Dependency tree · 2 levels

Sources