14 citations · 74 across the 28 of their papers we have counts for
30 papers · 1 filter
Locally injective semialgebraic maps
E. Baro, J. F. Fernando, J. M. Gamboa
We characterize locally injective semialgebraic maps between two semialgebraic sets in terms of the induced homomorphism between their rings of (continuous) semialgebraic functions…
Intermediate algebras of semialgebraic functions
E. Baro, J. F. Fernando, J. M. Gamboa
We characterize intermediate -algebras between the ring of semialgebraic functions and the ring of bounded semialgebraic funct…
On polynomial images of a closed ball
José F. Fernando, Carlos Ueno
In this work we approach the problem of determining which (compact) semialgebraic subsets of are images under polynomial maps of t…
Representation of positive semidefinite elements as sum of squares in 2-dimensional local rings
José F. Fernando
A classical problem in real geometry concerns the representation of positive semidefinite elements of a ring as sums of squares of elements of . If is an excellent ring…
Unbounded convex polyhedra as polynomial images of Euclidean spaces
José F. Fernando, J. M. Gamboa, Carlos Ueno
In a previous work we proved that each -dimensional convex polyhedron and its relative interior are regular images of . As the i…
Nash uniformization of chessboard sets by Nash manifolds with corners
Antonio Carbone, José F. Fernando
Bierstone and Parusiński studied the desingularization of -dimensional closed subanalytic sets and in particular of -dimensional closed semialgebraic sets. Their main tools a…
Surjective Nash maps between semialgebraic sets
Antonio Carbone, José F. Fernando
In this work we study the existence of surjective Nash maps between two given semialgebraic sets and . Some key ingredients are: the irreducible compon…
Topics in global real analytic geometry
F. Acquistapace, F. Broglia, J. F. Fernando
In the first half of twentieth century the theory of complex analytic functions and of their zerosets was fully developed. The definition of holomorphic function has a local nature…
Spectral maps associated to semialgebraic branched coverings
E. Baro, Jose F. Fernando, J. M. Gamboa
In this article we prove that a semialgebraic map is a branched covering if and only if its associated spectral map is a branched covering. In addition, such spectral map has a nea…
Rings of differentiable semialgebraic functions
E. Baro, José F. Fernando, J. M. Gamboa
In this work we analyze the main properties of the Zariski and maximal spectra of the ring of differentiable semialgebraic functions of class o…
Differentiable approximation of continuous semialgebraic maps
José F. Fernando, Riccardo Ghiloni
In this work we approach the problem of approximating uniformly continuous semialgebraic maps from a compact semialgebraic set to an arbitrary semialgebraic set …
On the set of local extrema of a subanalytic function
José F. Fernando
Let be a category of subanalytic subsets of real analytic manifolds that is closed under basic set-theoretical and basic topological operations. Let be a real a…
On regulous and regular images of Euclidean spaces
José Fernando, Goulwen Fichou, Ronan Quarez +1
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 regulo…
Normalization of complex analytic spaces from a global viewpoint
Francesca Acquistapace, Fabrizio Broglia, José F. Fernando
In this work we study some algebraic and topological properties of the ring of global analytic functions of the normalization of a re…
On the remainder of the semialgebraic Stone-Cěch compactification of a semialgebraic set
José F. Fernando, J. M. Gamboa
In this work we analyze some topological properties of the remainder of the semialgebraic Stone-Cěch compactification of a semialgebraic…
The open quadrant problem: A topological proof
Jose F. Fernando, J. M. Gamboa, Carlos Ueno
In this work we present a new polynomial map whose image is the open quadrant . The proof of this fact…
On Nash images of Euclidean spaces
José F. Fernando
In this work we characterize the subsets of that are images of Nash maps . We prove Shiota's conjecture and show that a subset ${\m…
On the irreducible components of globally defined semianalytic sets
José F. Fernando
In this work we present the concept of amenable -semianalytic subset of a real analytic manifold and study the main properties of this type of sets. Amenable -semianalyti…
On globally defined semianalytic sets
Francesca Acquistapace, Fabrizio Broglia, José F. Fernando
In this work we present the concept of -semianalytic subset of a real analytic manifold and more generally of a real analytic space. -semianalytic sets can be understood as t…
A short proof for the open quadrant problem
Jose F. Fernando, Carlos Ueno
In 2003 it was proved that the open quadrant of is a polynomial image of . This result was the origin of an ulterior more systematic st…
On complements of convex polyhedra as polynomial images of
José F. Fernando, Carlos Ueno
In this work we prove constructively that the complement of an -dimensional unbounded convex polyhedron a…
On spectral types of semialgebraic sets
José F. Fernando, J. M. Gamboa
In this work we prove that a semialgebraic set is determined (up to a semialgebraic homeomorphism) by its ring of (continuous) semialgebra…
On the substitution theorem for rings of semialgebraic functions
Jose F. Fernando
Let be an extension of real closed fields and the ring of (continuous) semialgebraic functions on a semialgebraic set . We prove that…
Approximation on Nash sets with monomial singularities
Elías Baro, José F. Fernando, Jesús M. Ruiz
This paper is devoted to the approximation of differentiable semialgebraic functions by Nash functions. Approximation by Nash functions is known for semialgebraic functions defined…