Sous-ensembles analytiques d'une variete banachique complexe [Hardcover]

This book gives an exposition of A. Douady's works in the theory of Banach analytic varieties. It presents his treatments of germs of analytic mappings and functions, and studies on local properties of analytic subsets of a Banach variety. Among beautiful results it was shown that every compact metrizable space is homeomorphic to an analytic subsets of Banach space.  A. Douady has developed function theory along classical lines: Quasi-finite  implies finite for certain analytic maps: Noether normalization; Hilbert Nullstellenansatz. and provided extensions of analytic subsets and holomorphic or meromorphic  functions a la Remmert-Stein-Chow.