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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.

On definably proper maps

Mário J. EdmundoMarcello MaminoLuca Prelli — 2016

Fundamenta Mathematicae

In this paper we work in o-minimal structures with definable Skolem functions, and show that: (i) a Hausdorff definably compact definable space is definably normal; (ii) a continuous definable map between Hausdorff locally definably compact definable spaces is definably proper if and only if it is a proper morphism in the category of definable spaces. We give several other characterizations of definably proper, including one involving the existence of limits of definable types. We also prove the...

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