Caractérisation des simplexes par des propriétés portant sur les faces fermées et sur les ensembles compacts de points extremaux.
Carathéodory's and Helly's dimensions of products of convexity structures
Cardinality of some convex sets and of their sets of extreme points
We show that the cardinality of a compact convex set W in a topological linear space X satisfies the condition that . We also establish some relations between the cardinality of W and that of extrW provided X is locally convex. Moreover, we deal with the cardinality of the convex set E(μ) of all quasi-measure extensions of a quasi-measure μ, defined on an algebra of sets, to a larger algebra of sets, and relate it to the cardinality of extrE(μ).
Central points of convex sets
Characterizations of convex vector functions and optimization.
Characterizations of reduced polytopes in finite-dimensional normed spaces.
Characterizations of ultrabarrelledness and barrelledness involving the singularities of families of convex mappings.
Characterizing certain staircase convex sets in .
Characterizing dominates on a family of triangular norms.
Choquet theory in metric spaces.
Choquetova teorie a Dirichletova úloha
Chords and arclength of a closed space curve
Circles holding a regular triangular prism.
Circumradius versus side lengths of triangles in linear normed spaces
Given a planar convex body B centered at the origin, we denote by ℳ ²(B) the Minkowski plane (i.e., two-dimensional linear normed space) with the unit ball B. For a triangle T in ℳ ²(B) we denote by the least possible radius of a Minkowskian ball enclosing T. We remark that in the terminology of location science is the optimum of the minimax location problem with distance induced by B and vertices of T as existing facilities (see, for instance, [HM03] and the references therein). Using methods...
Circumscribed simplices of minimal mean width.
Circumscribing constant-width bodies with polytopes.
Classical solids.
Classification of Arrangements by the Number of Their Cells.
Closures of faces of compact convex sets
This paper gives necessary and sufficient conditions for the closure of a face in a compact convex set to be again a face. As applications of these results, several theorems scattered in the literature are proved in an economical and uniform manner.
Clusters minimizing area plus length of singular curves.