DefinitionDefinition: AI-adaptedProof: Not applicableSession-authored (Fable 5 assisted)audited 2026-08-02

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.

The evaluation map from a space into the unit cube indexed by a family of continuous functions

Definition

For a family $\mathcal F$ of maps $f:X\to[0,1]$ , its evaluation map is $e_{\mathcal F}:X\longrightarrow[0,1]^{\mathcal F},\qquad e_{\mathcal F}(x)(f)=f(x).$ The target has the product topology (The product set $\prod_{i \in I} X_i$ 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). The formula is a function because each value $f(x)$ lies in $[0,1]$ ; if $\mathcal F=\varnothing$ , its target is the one-element empty product and the formula still defines the unique map to it.

Depends on

Used by

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 34 results over 9 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

E. Moorhouse, The Stone–Čech Compactification (standard reference, not scraped)