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.
Uniformizable and separated-uniformizable topological spaces
Definition
A topological space is uniformizable if its topology is induced by some uniformity (The sets containing an entourage ball about each of their points form a topology). It is separated-uniformizable if it is induced by a separated uniformity (Separated uniformity: the intersection of all entourages is the diagonal).
Depends on
Used by
- FALSE: every uniformizable topology has a unique compatible uniformity False statement
- Assuming dependent choice, every uniformizable space is completely regular Lemma
- Every uniformizable space is regular Lemma
- A nonempty compact Hausdorff space carries exactly one compatible uniformity Theorem
- Assuming dependent choice, a nonempty topological space is uniformizable if and only if it is completely regular Theorem
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 16 results over 12 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)
- M. Kunzinger, General Topology (standard reference, not scraped)