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On globally defined semianalytic sets

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Acquistapace, Francesca and Broglia, Fabrizio and Fernando Galván, José Francisco (2015) On globally defined semianalytic sets. Mathematische Annalen . pp. 1-42. ISSN 0025-5831

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Official URL: http://link.springer.com/article/10.1007%2Fs00208-015-1342-5#page-1


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Abstract

In this work we present the concept of C-semianalytic subset of a real analytic manifold and more generally of a real analytic space. C-semianalytic sets can be understood as the natural generalization to the semianalytic setting of global analytic sets introduced by Cartan (C-analytic sets for short). More precisely S is a C-semianalytic subset of a real analytic space (X, OX ) if each point of X has a neighborhood U such that S ∩ U is a finite boolean combinations of global analytic equalities and strict inequalities on X. By means of paracompactness C-emianalytic sets are the locally finite unions of finite boolean combinations of global analytic equalities and strict inequalities on X. The family of C-semianalytic sets is closed.


Item Type:Article
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:35249
Deposited On:01 Feb 2016 08:15
Last Modified:01 Feb 2016 09:57

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