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Quelques propriétés des applications analytiques près d’un homéomorphisme. (French) Zbl 0579.32042
Suppose that $$\phi$$ : $$V\to W$$ is a homeomorphism between two (real or complex) analytic spaces. This paper is concerned with the question whether any analytic map $$\psi$$ : $$V\to W$$ sufficiently close to $$\phi$$ must also be a homeomorphism. The author proves that if $$\psi$$ : $$V\to W$$ is an algebraic map between complex projective varieties which induces an isomorphism on integral homology then $$\psi$$ is an algebraic isomorphism. It is also proved that if $$\psi$$ is an analytic map between connected compact real analytic spaces which induces an isomorphism on $${\mathbb{Z}}_ 2$$-homology and if $$\psi$$ restricts to an isomorphism from $$V-S$$ to $$W- \psi (S)$$ for some proper analytic subspace S of V, then $$\psi$$ is a homeomorphism.
Reviewer: F.Kirwan
##### MSC:
 32H99 Holomorphic mappings and correspondences 32C15 Complex spaces 14E05 Rational and birational maps 32C05 Real-analytic manifolds, real-analytic spaces 32J99 Compact analytic spaces