2 citations · 4 across the 9 of their papers we have counts for
13 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…
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.…
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…
Approximation of maps into spheres by piecewise-regular maps of class C^k
Marcin Bilski
The aim of this paper is to prove that every continuous map from a compact subset of a real algebraic variety into a sphere can be approximated by piecewise-regular maps of class C…
Effective approximation of the solutions of algebraic equations
Marcin Bilski, Peter Scheiblechner
Let F be a holomorphic map whose components satisfy some polynomial relations. We present an algorithm for constructing Nash maps locally approximating F, whose components satisfy…
Higher order approximation of analytic sets by topologically equivalent algebraic sets
Marcin Bilski, Krzysztof Kurdyka, Adam Parusinski +1
It is known that every germ of an analytic set is homeomorphic to the germ of an algebraic set. In this paper we show that the homeomorphism can be chosen in such a way that the an…