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 inverse limit has its canonical coordinate projection maps
Definition
For an inverse limit , the th coordinate projection is
Because elements of are tuples, each projection is simply the ambient Cartesian-product coordinate map restricted to the compatible-tuples subset (The inverse limit is the set of compatible tuples in the Cartesian product).
Depends on
Used by
- FALSE: every inverse limit of surjective finite-group systems has surjective coordinate projections in ZF False statement
- The kernels of the finite coordinate projections form an open normal neighbourhood basis at the identity Lemma
- A map into an inverse limit is continuous exactly when all coordinate composites are continuous Theorem
- The compatible-tuple construction satisfies the inverse-limit universal property in groups Theorem
Dependency tree · two levels
3 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
- Brian Osserman, Math 6112 notes on inverse limits and profinite groups (standard reference, not scraped)
- H. W. Lenstra, Profinite groups and Galois groups (standard reference, not scraped)