3 citations · 5 across the 13 of their papers we have counts for
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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…