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Let ??Rn be a compact Nash manifold; A,B the rings of Nash, analytic global functions on ?. The main result of this paper is the following: Theorem 1. Let ?,?? be a pair of Nash submanifolds of some Rn ,Rq and let us suppose ? is compact. Let F1[...]texto impreso
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 noetheriann[...]texto impreso
Let M superset-of R be a compact Nash manifold, and N (M) [resp. O(M)] its ring of global Nash (resp. analytic) functions. A global Nash (resp. analytic) set is the zero set of finitely many global Nash (resp. analytic) functions, and we have th[...]texto impreso
Nash functions are those real analytic functions which are algebraic over the polynomials. Let M?Rn be a Nash manifold, N(M) the ring of Nash functions on M and O(M) the ring of analytic functions on M. The following problems have been open for [...]texto impreso
We show that the complexity of semialgebraic sets and mappings can be used to parametrize Nash sets and mappings by Nash families. From this we deduce uniform bounds on the complexity of Nash functions that lead to first-order descriptions of ma[...]
