Displaying similar documents to “Nash functions on noncompact Nash manifolds”

Nash triviality in families of Nash mappings

Jesús Escribano (2001)

Annales de l’institut Fourier

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We study triviality of Nash families of proper Nash submersions or, in a more general setting, the triviality of pairs of proper Nash submersions. We work with Nash manifolds and mappings defined over an arbitrary real closed field R . To substitute the integration of vector fields, we study the fibers of such families on points of the real spectrum R p ˜ and we construct models of proper Nash submersions over smaller real closed fields. Finally we obtain results on finiteness of topological...

Global problems on Nash functions.

Michel Coste, Jesús M. Ruiz, Masahiro Shiota (2004)

Revista Matemática Complutense

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This is a survey on the history of and the solutions to the basic global problems on Nash functions, which have been only recently solved, namely: separation, extension, global equations, Artin-Mazur description and idempotency, also noetherianness. We discuss all of them in the various possible contexts, from manifolds over the reals to real spectra of arbitrary commutative rings.

Classification of Nash manifolds

Masahiro Shiota (1983)

Annales de l'institut Fourier

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A semi-algebraic analytic manifold and a semi-algebraic analytic map are called a Nash manifold and a Nash map respectively. We clarify the category of Nash manifolds and Nash maps.

Modified Nash triviality of a family of zero-sets of real polynomial mappings

Toshizumi Fukui, Satoshi Koike, Masahiro Shiota (1998)

Annales de l'institut Fourier

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In this paper we introduce the notion of modified Nash triviality for a family of zero sets of real polynomial map-germs as a desirable one. We first give a Nash isotopy lemma which is a useful tool to show triviality. Then, using it, we prove two types of modified Nash triviality theorem and a finite classification theorem for this triviality. These theorems strengthen similar topological results.