4 papers
A simplified proof of the o-minimal Whitney Extension Theorem
Beata Kocel-Cynk, Wiesław Pawłucki, Anna Valette
We give a proof of the o-minimal version of the Whitney Extension Theorem simplified as compared to the original ones. A new simplifying ingredient is a definable variant of Urysoh…
Semialgebraic Calderon-Zygmund theorem on regularization of the distance function
Beata Kocel-Cynk, Wiesław Pawłucki, Anna Valette
We prove that, for any closed semialgebraic subset of and for any positive integer , there exists a Nash function $f:\mathbb{R}^n\setminus W\longrightarrow (0…
Differentiable functions defined in closed sets. A problem of Whitney
E. Bierstone, P. D. Milman, W. Pawlucki
In 1934, Whitney raised the question of how to recognize whether a function f defined on a closed subset X of Euclidean space is the restriction of a function that is continuously…
Composite Differentiable Functions
Edward Bierstone, Pierre D. Milman, Wieslaw Pawlucki
We introduce a new point of view towards Glaeser's theorem on composite functions [Ann. of Math. 1963], with respect to which we can formulate a `` composite functi…