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.
Closed subspaces inherit normality: compact intervals, ordinal endpoints, and finite closed pieces
Example
In a compact Hausdorff space, normality follows from A compact Hausdorff space is regular and normal, hence and . Any closed interval inside a compact ordered interval, any closed endpoint set, and every finite closed subset therefore inherit normality through Every closed subspace of a normal space is normal.
The qualification “closed” is essential. The deleted Tychonoff plank on the A page is an open subspace of a compact Hausdorff normal space but is not normal, so the example cannot be strengthened by replacing “closed” with “arbitrary”.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
13 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
- J. R. Munkres, Topology, 2nd ed., §31 (standard reference, not scraped)
- Normal space (Wikipedia) (standard reference, not scraped)
- Tychonoff plank (Wikipedia) (standard reference, not scraped)