Douady's conjecture on Banach analytic spaces
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 June 1994
 arXiv:
 arXiv:functan/9406004
 Bibcode:
 1994funct.an..6004P
 Keywords:

 Mathematics  Functional Analysis
 EPrint:
 5 pages. AmS TeX 2.1 source file