Douady's conjecture on Banach analytic spaces
Abstract
Description
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.
5 pages. AmS TeX 2.1 source file
5 pages. AmS TeX 2.1 source file