Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge 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.
Cauchy filter in a uniform space
Definition
A filter on a uniform space is Cauchy if for every entourage some satisfies . Such an is an -small member of .
Depends on
Used by
- Complete uniform space: every Cauchy filter converges Definition
- A Cauchy filter with a cluster point converges to that point Lemma
- Every Cauchy filter canonically determines a unique minimal Cauchy filter coarser than it Lemma
- Every convergent filter on a uniform space is Cauchy Lemma
- Every ultrafilter on a totally bounded uniform space is Cauchy Lemma
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 19 results over 7 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.
Sources
- J. Wodzicki, Uniform Structure (standard reference, not scraped)
- Encyclopedia of Mathematics, Uniform space (standard reference, not scraped)