1994/06/20 by Vladimir Pestov, Pestov, Vladimir G.
Mathematics · #Advanced Banach Space Theory #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.funct-an/9406004
openalex publication_date 1994/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that, as conjectured by Adrien Douady back in 1972, every complete metric space is homeomorphic (moreover, isometric) to the locus of zeros of an analytic map between two Banach spaces. As a corollary, a paracompact topological space admits the structure of a Banach analytic space if and only if it is metrizable with a complete metric.