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Grauert's theorem for subanalytic open sets in real analytic manifolds

Daniel BarletTeresa Monteiro Fernandes — 2011

Studia Mathematica

By an open neighbourhood in ℂⁿ of an open subset Ω of ℝⁿ we mean an open subset Ω' of ℂⁿ such that ℝⁿ ∩ Ω' = Ω. A well known result of H. Grauert implies that any open subset of ℝⁿ admits a fundamental system of Stein open neighbourhoods in ℂⁿ. Another way to state this property is to say that each open subset of ℝⁿ is Stein. We shall prove a similar result in the subanalytic category: every subanalytic open subset in a paracompact real analytic manifold M admits a fundamental system of subanalytic...

Relative subanalytic sheaves

Teresa Monteiro FernandesLuca Prelli — 2014

Fundamenta Mathematicae

Given a real analytic manifold Y, denote by Y s a the associated subanalytic site. Now consider a product Y = X × S. We construct the endofunctor S on the category of sheaves on Y s a and study its properties. Roughly speaking, S is a sheaf on X s a × S . As an application, one can now define sheaves of functions on Y which are tempered or Whitney in the relative sense, that is, only with respect to X.

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