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Andradas Heranz, Carlos and 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

PDF
187kB |

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

## Abstract

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.

Item Type: | Article |
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Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 14768 |

Deposited On: | 18 Apr 2012 08:23 |

Last Modified: | 06 Aug 2018 11:49 |

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