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 locally metrizable space: every point has a metrizable open neighbourhood
Definition
A topological space is locally metrizable if every belongs to an open set whose subspace topology (Subspace topology: the traces of the open sets, its closed sets and its bases, the continuity of the inclusion, and the characteristic property of a map into a subspace) is metrizable (Metrizable space: a topological space whose topology is induced by some metric; metrizability is topological, the metric is not). Thus is an open neighbourhood of in the convention of Neighbourhood of a point and neighbourhood base, with this library's convention that a neighbourhood need not be open; no global metric on is part of the definition.
Depends on
- Neighbourhood of a point and neighbourhood base, with this library's convention that a neighbourhood need not be open
- Subspace topology: the traces of the open sets, its closed sets and its bases, the continuity of the inclusion, and the characteristic property of a map into a subspace
- Metrizable space: a topological space whose topology is induced by some metric; metrizability is topological, the metric is not
Used by
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 63 results over 13 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
- R. Engelking, General Topology, metrization theorems (standard reference, not scraped)