AWhat changed
Unifies normality and second countability into an explicit metrization criterion, with a countable continuous-separator construction and two-direction topology compatibility.
Scientific scope
Unifies normality and second countability into an explicit metrization criterion, with a countable continuous-separator construction and two-direction topology compatibility. The exact 1925 target is the normal, second-countable Hausdorff-space criterion in printed 310 Hauptsatz and its countable-separator metric construction, not an unqualified attribution of the later familiar regular-second-countable theorem. Printed 315 explicitly asks whether regularity alone together with a countable base suffices; this paper does not resolve that weaker assumption. Countable dense subsets alone cannot replace a countable base for arbitrary topological spaces, as its printed 310 footnote notes. Hausdorff separation used in printed 312 is retained; modern non-Hausdorff spaces are not admitted. Continuous closed-set separation is an inherited earlier Urysohn lemma reproved here, not a separately duplicated achievement. The compact-space corollary uses the historical Hausdorff setting and is not extended to arbitrary modern non-Hausdorff compact spaces. Original byline remains Urysohn, while Alexandroff's explicit posthumous scientific redaction is retained in the narrative credit rather than silently added as an original coauthor.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- Paul Urysohn · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- Paul Urysohn, Zum Metrisationsproblem, Mathematische Annalen 94(1925),309–315: original-page GDZ OCR
- Eu DML bibliographic record for Zum Metrisationsproblem
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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