Douady's conjecture on Banach analytic spaces

Details Douady's conjecture on Banach analytic spaces Douady's conjecture on Banach analytic spaces

1994-06-20

arxiv.org/abs/funct-an/9406004v1

Mathematics

Functional Analysis

5 pages. AmS TeX 2.1 source file

Scientific paper

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.

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