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A set which can be defined by systems of polynomial inequalities is called semialgebraic. When such a scription is possible locally around every point, by means of analytic inequalities varying with the point, the set; is called semianalytic. If[...]texto impreso
A semialgebraic set is called basic if it can be described by a single system of strict polynomial inequalities. A semianalytic set is called basic if it can be described by a system of strict real analytic inequalities in a neighborhood of each[...]texto impreso
The classical Whitney approximation theorem states that a smooth function function f: Rn - R can be approximated by analytic functions. We prove that these analytic functions approximating f can be taken aas real holomorphic functions on the who[...]texto impreso
Andradas Heranz, Carlos ; Recio, Tomás ; Sendra, J. Rafael | Association for Computing Machinery | 1999Given a variety V, implicitly defined over an algebraic separable field extension k(alpha), A. Weil [5] developed a restriction technique (called by him a descente method),that associates to V a suitable k-variety W, such that many properties of[...]texto impreso
We show that the closed stability index of an excellent henselian local ring of real dimension d> 2 with real closed residue field is (s) over bar (A) = 1/2d(d+1). When d=2 it is shown that the value of can be either 2 or 3 and give characteriza[...]texto impreso
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 [...]texto impreso
Let M be a connected paracompact real analytic manifold and S a semi-analytic subset. The following results are proved: 1) If dim(M) = 2 and S is globally semianalytic, then every connected component of S is again globally semianalytic. 2) S is [...]texto impreso
The evolution of knowledge and technology in recent decades has brought profound changes in science policy, not only in the countries but also in the supranational organizations. It has been necessary, therefore, to adapt the scientific institut[...]texto impreso
Let X be a real affine algebraic set and S a semialgebraic set. Many important results are known about the basicness of S: mainly, if S is basic open, S can be defined by s strict inequalities, where s is bounded by the dimension of X. It is als[...]texto impreso
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We prove that any regularly closed semialgebraic set of R", where R is any real closed field and regularly closed means that it is the closure of its interior, is the projection under a finite map of an irreducible algebraic variety in some Rn +[...]texto impreso
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The main application of the results of this paper is to prove the existence of real valuation rings of the quotient field K of an excellent domain A having prescribed centers, ranks, rational ranks and residue dimensions. The major part of the p[...]texto impreso
The invariant p(V ) has been introduced by M. Marshall as a measure of the complexity of semialgebraic sets of a real algebraic variety V . This invariant is defined as the least integer such that every semialgebraic set S ? V has a separating f[...]
