In this work we approach the problem of determining which (compact) semialgebraic
subsets of Rn are images under polynomial maps f: Rm→ Rn of the closed unit ball Bm …

In this work we study the existence of surjective Nash maps between two given
semialgebraic sets S and T. Some key ingredients are: the irreducible components S i⁎ of S …

In this work we prove constructively that the complement \mathbbR^n\\mathcalK of a convex
polyhedron \mathcalK⊂\mathbbR^n and the complement \mathbbR^n\Int(\mathcalK) of its …

In this work we prove that the set of points at infinity S_ ∞:=\; Cl _\mathbb R\mathbb P^ m (S)
∩ H _ ∞ S∞:= Cl RP m (S)∩ H∞ of a semialgebraic set S ⊂\mathbb R^ m S⊂ R m that is …

In this work we compare the semialgebraic subsets that are images of regulous maps with
those that are images of regular maps. Recall that a map f: R n→ R m is regulous if it is a …

In this work we characterize the subsets of R n that are images of Nash maps f: R m→ R n.
We prove Shiota's conjecture and show that a subset S⊂ R n is the image of a Nash map f …

In 2003 it was proved that the open quadrant Q:={x> 0, y> 0} of R 2 is a polynomial image of
R 2. This result was the origin of an ulterior more systematic study of polynomial images of …

Let be a convex polyhedron of dimension n. Denote and let be its closure. We prove that for
n= 3 the semialgebraic sets and are polynomial images of ℝ3. The former techniques cannot …

The study of the topology of polynomial maps originates from classical questions in affine
geometry, such as the Jacobian Conjecture, as well as from works of Whitney, Thom, and …

We prove constructively that: The complement R^ n ∖ KR n\K of an n-dimensional
unbounded convex polyhedron K ⊂ R^ n K⊂ R n and the complement R^ n ∖ Int (K) R n\Int …