Alphabeta Math
DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (z-ai/glm-5.2)audited 2026-07-31
How 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.

Topological group: multiplication and inversion are continuous

Definition

A topological group is a group GG (Group and abelian group) with a topology such that multiplication m:G×G→Gm:G\times G\to G, m(x,y)=xym(x,y)=xy, and inversion ι:G→G\iota:G\to G, ι(x)=x−1\iota(x)=x^{-1}, are continuous (Continuity of a map of topological spaces at a point and globally) for the product topology (The product set ∏i∈IXi\prod_{i \in I} X_i of functions choosing a point in each factor, the projections, the box topology, and the product topology as the initial topology of the projections; the empty product is a one-point space).

Depends on

Used by

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 37 results over 10 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources