Displaying similar documents to “Nash triviality in families of Nash mappings”

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.

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.

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.

A note on global Nash subvarieties and Artin-Mazur theorem

Alessandro Tancredi, Alberto Tognoli (2004)

Bollettino dell'Unione Matematica Italiana

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It is shown that every connected global Nash subvariety of R n is Nash isomorphic to a connected component of an algebraic variety that, in the compact case, can be chosen with only two connected components arbitrarily near each other. Some examples which state the limits of the given results and of the used tools are provided.