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Complexity of global semianalytic sets in a real analytic manifold of dimension 2

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Andradas Heranz, Carlos y Díaz-Cano Ocaña, Antonio (2001) Complexity of global semianalytic sets in a real analytic manifold of dimension 2. Journal für die reine und angewandte Mathematik, 534 . pp. 195-208. ISSN 0075-4102

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URL Oficial: http://www.degruyter.com/view/j/crll



Resumen

Let X subset of R-n be a real analytic manifold of dimension 2. We study the stability index of X, s(X), that is the smallest integer s such that any basic open subset of X can be written using s global analytic functions. We show that s(X) = 2 as it happens in the semialgebraic case. Also, we prove that the Hormander-Lojasiewicz inequality and the Finiteness Theorem hold true in this context. Finally, we compute the stability index for basic closed subsets, S, and the invariants t and (t) over bar for the number of unions of open (resp. closed) basic sets required to describe any open (resp. closed) global semianalytic set.


Tipo de documento:Artículo
Materias:Ciencias > Matemáticas > Geometria algebraica
Código ID:14768
Depositado:18 Abr 2012 08:23
Última Modificación:11 Nov 2013 14:28

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