28 citations · 50 across the 13 of their papers we have counts for
19 papers
Approximation of maps from algebraic polyhedra to real algebraic varieties
Marcin Bilski, Wojciech Kucharz
Given a finite simplicial complex in and a real algebraic variety by a -regular map we mean a continuous…
Spaces of maps between real algebraic varieties
Wojciech Kucharz
Given two real algebraic varieties X and Y, we denote by R(X,Y) the set of all regular maps from X to Y. The set R(X,Y) is regarded as a topological subspace of the space C(X,Y) of…
Approximation of maps between real algebraic varieties
Juliusz Banecki, Wojciech Kucharz
A nonsingular real algebraic variety Y is said to have the approximation property if for every real algebraic variety X the following holds: if f:X-->Y is a C^inf map that is homot…
Dominating real algebraic morphisms
Wojciech Kucharz
Let X and Y be nonsingular real algebraic varieties, dimX>dimY-1. Assume that the variety Y is malleable, compact and connected. Our main result implies that each regular map from…
Approximation and homotopy in regulous geometry
Wojciech Kucharz
Let X, Y be nonsingular real algebraic sets. A map fi:X-->Y is said to be k-regulous, where k is a nonnegative integer, if it is of class C^k and the restriction of fi to some Zari…
Hartogs-type theorems in real algebraic geometry, I
Marcin Bilski, Jacek Bochnak, Wojciech Kucharz
Let f:X-->R be a function defined on a connected nonsingular real algebraic set X in R^n. We prove that regularity of f can be detected on either algebraic curves or surfaces in X.…
Rational approximation of holomorphic maps
Jacek Bochnak, Wojciech Kucharz
Let X be a complex nonsingular affine algebraic variety, K a holomorphically convex subset of X, and Y a homogeneous variety for some complex linear algebraic group. We prove that…
On approximation of maps into real algebraic homogeneous spaces
Jacek Bochnak, Wojciech Kucharz
Let X be a compact (resp. compact and nonsingular) real algebraic variety and let Y be a homogeneous space for some linear real algebraic group. We prove that a continuous (resp. C…
Approximation by piecewise-regular maps
Marcin Bilski, Wojciech Kucharz
A real algebraic variety W of dimension m is said to be uniformly rational if each of its points has a Zariski open neighborhood which is biregularly isomorphic to a Zariski open s…
Checking real analyticity on surfaces
Jacek Bochnak, János Kollár, Wojciech Kucharz
We prove that a real-valued function (that is not assumed to be continuous) on a real analytic manifold is analytic whenever all its restrictions to analytic submanifolds homeomorp…
Nash regulous functions
Wojciech Kucharz
A real-valued function on R^n is k-regulous, where k is a nonnegative integer, if it is of class C^k and can be represented as a quotient of two polynomial functions on R^n. Severa…
Piecewise-regular maps
Wojciech Kucharz
Let V, W be real algebraic varieties (that is, up to isomorphism, real algebraic sets), and let X be a subset of V. A map f from X into W is said to be regular if it can be extende…
Regulous vector bundles
Wojciech Kucharz, Maciej Zieliński
Among recently introduced new notions in real algebraic geometry is that of regulous functions. Such functions form a foundation for the development of regulous geometry. Several i…
Linear equations on real algebraic surfaces
Wojciech Kucharz, Krzysztof Kurdyka
We prove that if a linear equation, whose coefficients are continuous rational functions on a nonsingular real algebraic surface, has a continuous solution, then it also has a cont…
Some conjectures on continuous rational maps into spheres
Wojciech Kucharz, Krzysztof Kurdyka
Recently continuous rational maps between real algebraic varieties have attracted the attention of several researchers. In this paper we continue the investigation of approximation…
Comparison of stratified-algebraic and topological K-theory
Wojciech Kucharz, Krzysztof Kurdyka
Stratified-algebraic vector bundles on real algebraic varieties have many desirable features of algebraic vector bundles but are more flexible. We give a characterization of the co…
Curve-rational functions
János Kollár, Wojciech Kucharz, Krzysztof Kurdyka
Let be a subset of the set of real points of a real algebraic variety . We investigate which functions are the restrictions of rational functions on …
Continuous rational maps into spheres
Wojciech Kucharz
Let X be a compact nonsingular real algebraic variety. We prove that if a continuous map from X into the unit p-sphere is homotopic to a continuous rational map, then, under certai…
Stratified-algebraic vector bundles
Wojciech Kucharz, Krzysztof Kurdyka
We investigate stratified-algebraic vector bundles on a real algebraic variety X. A stratification of X is a finite collection of pairwise disjoint, Zariski locally closed subvarie…