Displaying similar documents to “Grauert's theorem for subanalytic open sets in real analytic manifolds”

K-analytic versus ccm-analytic sets in nonstandard compact complex manifolds

Rahim Moosa, Sergei Starchenko (2008)

Fundamenta Mathematicae

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It is shown that in an elementary extension of a compact complex manifold M, the K-analytic sets (where K is the algebraic closure of the underlying real closed field) agree with the ccm-analytic sets if and only if M is essentially saturated. In particular, this is the case for compact Kähler manifolds.

The Lie group of real analytic diffeomorphisms is not real analytic

Rafael Dahmen, Alexander Schmeding (2015)

Studia Mathematica

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We construct an infinite-dimensional real analytic manifold structure on the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is defined to be real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known, the construction turns the group of real analytic diffeomorphisms into a smooth locally convex Lie group. We prove that this group is regular in the sense...

Extending analyticK-subanalytic functions

Artur Piękosz (2004)

Open Mathematics

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Letg:U→ℝ (U open in ℝn) be an analytic and K-subanalytic (i. e. definable in ℝanK, whereK, the field of exponents, is any subfield ofℝ) function. Then the set of points, denoted Σ, whereg does not admit an analytic extension is K-subanalytic andg can be extended analytically to a neighbourhood of Ū.