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.

Fréchet–Urysohn spaces and sequential spaces

Definition

A topological space $X$ is Fréchet–Urysohn if, whenever $p\in\overline A$ , there is a sequence in $A$ converging to $p$ . Equivalently, $\operatorname{seqcl}(A)=\overline A$ for every $A\subseteq X$ , since sequential closure is always contained in closure (The sequential closure is contained in the closure, continuity implies sequential continuity, and sequential limits need not be unique).

A subset $C\subseteq X$ is sequentially closed if every sequence in $C$ that converges in $X$ has its limit in $C$ . The space is sequential if every sequentially closed subset is closed. Equivalently, $\operatorname{seqcl}(A)=A$ implies $\overline A=A$ for every $A\subseteq X$ .

Depends on

Used by

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 55 results over 12 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

Sequential space (Wikipedia) (standard reference, not scraped)
Fréchet–Urysohn space (Wikipedia) (standard reference, not scraped)