3 citations · 5 across the 13 of their papers we have counts for
13 papers
Invariants of real affine varieties based on their complexifications
Juliusz Banecki
We introduce a new family of invariants of real algebraic sets defined in terms of the topology of their complexifications and compute some of these invariants for spheres. This al…
Optimal embedding dimension in the Nash--Tognoli theorem
Juliusz Banecki
We prove that every smooth compact submanifold of can be approximated up to a small isotopy by the real locus of a nonsingular complex algebraic subset of $\C^n$ defined ove…
Uniform rationality of products with the plane
Juliusz Banecki
Let be a nonsingular rational variety. We prove that is uniformly rational. It follows that nonsingular stably rational varieties are stably uniformly ra…
Homotopy properties of regular mappings into real retract rational varieties
Juliusz Banecki
We study homotopy properties of regular mappings from spheres into a real retract rational variety . We show that the homotopy classes which are represented by such mappings for…
Extension of -regulous functions from varieties of arbitrary dimension
Juliusz Banecki
We prove that a -regulous function defined on a non-singular affine variety can always be extended to the entire affine space.
Retract rational varieties are uniformly retract rational
Juliusz Banecki
We prove that nonsingular retract rational algebraic varieties over any infinite field are uniformly retract rational. As a consequence, every rational, projective, nonsingular com…
Relative Stone-Weierstrass theorem for mappings between varieties
Juliusz Banecki
We introduce a class of real algebraic varieties characterised by a simple rationality condition, which exhibit strong properties regarding approximation of continuous and smooth m…
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…
Separately regular and separately Nash functions
Juliusz Banecki
We strengthen certain known results saying that separately regular functions are rational and separately Nash functions are semialgebraic. The approach presented here unifies and h…
Algebraic homotopy classes
Juliusz Banecki
We prove several positive results regarding representation of homotopy classes of spheres and algebraic groups by regular mappings. Most importantly we show that every mapping from…
Extensions of k-regulous functions from two-dimensional varieties
Juliusz Banecki
We prove that a -regulous function defined on a two-dimensional non-singular affine variety can be extended to an ambient variety. Additionally we derive some results concerning…
Distortion in the group of circle homeomorphisms
Juliusz Banecki, Tomasz Szarek
Let be the group of piecewise--affine circle homeomorphisms or the group ${\Diff}^{\infty}(\mathbb R/\mathbb Z)$ of smooth circle diffeomorphisms. A c…
Sums of even powers of k-regulous functions
Juliusz Banecki, Tomasz Kowalczyk
We provide an example of a nonnegative -regulous function on for and which cannot be written as a sum of squares of -regulous functions. W…