9 citations · 15 across the 9 of their papers we have counts for
11 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…
Inner Lipschitz approximation in o-minimal structures
Nhan Nguyen, Anna Valette, Guillaume Valette
Given an o-minimal structure, we show that every definable (in this structure) mapping that is Lipschitz with respect to the inner metric can be approximated by map…
A remark on definable equivalence
Anna Valette, Guillaume Valette
We establish that if a submanifold of is definable in some o-minimal structure then any definable submanifold which is $\mathscr{C}^\inft…
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…
Uniform Poincaré inequality in o-minimal structures
Anna Valette, Guillaume Valette
We first define the trace on a domain which is definable in an o-minimal structure. We then show that every function vanishing on the boundary in the trace se…
Trace operators on bounded subanalytic manifolds
Anna Valette, Guillaume Valette
We prove that if is a bounded subanalytic submanifold of such that is connected for every and sma…
Poincaré inequality on subanalytic sets
Anna Valette, Guillaume Valette
Let be a subanalytic bounded open subset of , with possibly singular boundary. We show that given , there is a constant such that for any $u\…
Efroymson's approximation theorem for globally subanalytic functions
Anna Valette, Guillaume Valette
Efroymson's approximation theorem asserts that if is a semialgebraic mapping on a semialgebraic submanifold of and if $\…
A generalized Sard theorem on real closed fields
Anna Valette, Guillaume Valette
We work with semi-algebraic functions on arbitrary real closed fields. We generalize the notion of critical values and prove a Sard type theorem in our framework.
On a singular variety associated to a polynomial mapping
Nguyen Thi Bich Thuy, Anna Valette, Guillaume Valette
In the paper "Geometry of polynomial mapping at infinity via intersection homology" the second and third authors associated to a given polynomial mapping $F : \C^2 \to \C^2$ with n…
Geometry of polynomial mappings at infinity via intersection homology
Anna Valette, Guillaume Valette
For given polynomial map $F:\C^2\to\C^2$ with nonvanishing jacobian we associate a variety whose homology or intersection homology describes the geometry of singularities at infini…