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.
A finite discrete space is already its Stone–Čech compactification
Example
Let be a finite set with the discrete topology. Then its Stone–Čech compactification is itself.
Facts & Assumptions
Given: A finite discrete space .
A finite topological space is compact (Open cover, subcover, and compact topological space; a compact subset is a subspace that is compact in its own right).
Verification
Every two distinct points of a discrete space have disjoint singleton neighbourhoods, so is Hausdorff; it is compact by [L1].
The Stone–Čech compactification of a compact Hausdorff space adds no points applied to step 1.1 gives the claim.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
19 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
- E. Moorhouse, The Stone–Čech Compactification (standard reference, not scraped)