Theoreme de Pfister pour les varietes et anneaux de Witt reduits.
Topological methods in representation theory.
Topological types of fewnomials
Triangulation in o-minimal fields with standard part map
In answering questions of J. Maříková [Fund. Math. 209 (2010)] we prove a triangulation result that is of independent interest. In more detail, let R be an o-minimal field with a proper convex subring V, and let st: V → k be the corresponding standard part map. Under a mild assumption on (R,V) we show that a definable set X ⊆ Vⁿ admits a triangulation that induces a triangulation of its standard part st X ⊆ kⁿ.
Two interesting oriented matroids.
Une inégalité de Lojasiewicz effective
Whitney triangulations of semialgebraic sets
A compact semialgebraic set admits a semialgebraic triangulation such that the family of open simplexes forms a Whitney stratification and is compatible with a finite number of given semialgebraic subsets.
Zero-set property of o-minimal indefinitely Peano differentiable functions
Given an o-minimal expansion ℳ of a real closed field R which is not polynomially bounded. Let denote the definable indefinitely Peano differentiable functions. If we further assume that ℳ admits cell decomposition, each definable closed subset A of Rⁿ is the zero-set of a function f:Rⁿ → R. This implies approximation of definable continuous functions and gluing of functions defined on closed definable sets.
Нахождение компонент связности полуалгебраического множества в субэкспоненциальное время
Поиск кратчайшего пути вокруг полуалгебраических препятствий на плоскости
Полуалгебраические множества и варианты теоремы Тарского-Зайденберга-Макинтайра