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.
Under choice, for an infinite discrete space of cardinality , while
Example
For an infinite discrete of cardinality , singletons force every basis, dense set, singleton cover, and cellular family to have size . At a point, is a one-member local base. Hence and .
Depends on
- Under choice, weight $w(X)$, density $d(X)$, local character $\chi(x,X)$, and character $\chi(X)$ as raw cardinal minima and a supremum
- Under choice, Lindelöf degree $L(X)$ and cellularity $c(X)$ as raw cardinal functions
- The discrete, indiscrete, cofinite, cocountable, particular-point and Sierpinski topologies
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
20 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
- D. H. Fremlin, Measure Theory, Chapter 5A (standard reference, not scraped)
- Cardinal function (Wikipedia) (standard reference, not scraped)