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.
The -topology on is not uniformizable
Statement refuted
The -topology on is uniformizable.
Facts & Assumptions
Given: The -topology on .
Every uniformizable space is regular (Every uniformizable space is regular).
The -topology is Hausdorff and not regular (The -topology on , generated by the open intervals together with their complements of , is and Hausdorff but not regular).
Counterexample
Suppose the -topology were uniformizable.
It would be regular by [L1].
This contradicts its nonregularity in [L2].
Therefore the supposition is false, and the -topology is not uniformizable.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
25 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- R. Gardner, Introduction to Topology, notes on Munkres Section 31: The Separation Axioms (East Tennessee State University) (standard reference, not scraped)
- M. Kunzinger, General Topology (standard reference, not scraped)