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In this work we prove constructively that the complement $\R^n\setminus\pol$ of a convex polyhedron $\pol\subset\R^n$ and the complement $\R^n\setminus\Int(\pol)$ of its interior are regular images of $\R^n$. If $\pol$ is moreover bounded, we ca[...]texto impreso
In this work we prove constructively that the complement Rn \ K of a convex polyhedron K ? Rn and the complement Rn \ Int(K) of its interior are regular images of Rn. If K is moreover bounded, we can assure that Rn \ K and Rn \ Int(K) are also p[...]texto impreso
Fernando Galván, José Francisco ; Gamboa, J. M. ; Ueno, Carlos | Oxford University Press (OUP) | 2011We show that convex polyhedra in R(n) and their interiors are images of regular maps R(n) -> R(n). As a main ingredient in the proof, given an n-dimensional, bounded, convex polyhedron K subset of R(n) and a point p is an element of R(n) \ K, w[...]texto impreso
Let K Rn be a convex polyhedron of dimension n. Denote S := RnK and let S be its closure. We prove that for n = 3 the semialgebraic sets S and S are polynomial images of 3. The former techniques cannot be extended in general to represent the sem[...]texto impreso
In this work we prove that the set of points at infinity of a semialgebraic set that is the image of a polynomial map is connected. This result is no longer true in general if is a regular map. However, it still works for a large family of regul[...]texto impreso
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We present several obstructions for a subset S of Rm to be the image of an euclidean space Rn via a polynomial or a regular map f: Rn--> Rm, in terms of the "geometry" of its exterior boundary dS:=ClRm(S)\S
