Crossing patterns of semi-algebraic sets
نویسندگان
چکیده
منابع مشابه
Crossing patterns of semi-algebraic sets
We prove that, for every family F of n semi-algebraic sets in R of constant description complexity, there exist a positive constant ε that depends on the maximum complexity of the elements of F , and two subfamilies F1,F2 ⊆ F with at least εn elements each, such that either every element of F1 intersects all elements of F2 or no element of F1 intersects any element of F2. This implies the exist...
متن کاملAlgebraic boundaries of convex semi-algebraic sets
We study the algebraic boundary of a convex semi-algebraic set via duality in convex and algebraic geometry. We generalise the correspondence of facets of a polytope with the vertices of the dual polytope to general semi-algebraic convex sets. In this case, exceptional families of extreme points might exist and we characterise them semi-algebraically. We also give a strategy for computing a com...
متن کاملSemi-algebraic neighborhoods of closed semi-algebraic sets
— Given a closed (not necessarly compact) semi-algebraic set X in Rn, we construct a non-negative semi-algebraic C2 function f such that X=f−1(0) and such that for δ > 0 sufficiently small, the inclusion of X in f−1([0, δ]) is a retraction. As a corollary, we obtain several formulas for the Euler characteristic of X. Résumé. — Étant donné un ensemble semi-algébrique fermé (non nécessairement co...
متن کاملReal Homotopy Theory of Semi-algebraic Sets
We complete the details of a theory outlined by Kontsevich and Soibelman that associates to a semi-algebraic set a certain graded commutative differential algebra of “semi-algebraic differential forms” in a functorial way. This algebra encodes the real homotopy type of the semialgebraic set in the spirit of the DeRham algebra of differential forms on a smooth manifold. Its development is needed...
متن کاملComputing Roadmaps of General Semi-Algebraic Sets
In this paper we study the problem of determining whether two points lie in the same connected component of a semi-algebraic set S. Although we are mostly concerned with sets S , our algorithm can also decide if points in an arbitrary set S R can be joined by a semi-algebraic path, for any real closed eld R. Our algorithm computes a one-dimensional semi-algebraic subset <(S) of S (actually of a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2005
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2004.12.008