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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

## 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 |
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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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