-minimal pairs of compact convex sets.
Caractérisation des simplexes par des propriétés portant sur les faces fermées et sur les ensembles compacts de points extremaux.
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).
Choquet theory in metric spaces.
Compactness and extreme points of the set of quasi-measure extensions of a quasi-measure [Book]
Concerning interior mapping theorem
Cônes asymptotes d'ensembles non convexes
Congruence relations on cone semigroups.
Constant and variable drop theorems on metrizable locally convex spaces
Constant selections and minimax inequalities
In this paper, we establish two constant selection theorems for a map whose dual is upper or lower semicontinuous. As applications, matching theorems, analytic alternatives, and minimax inequalities are obtained.
Contrôle optimal dans des systèmes gouvernés par des inéquations variationnelles
Convex analysis for sets of local martingales measures
Convex cones in finite-dimensional real vector spaces
Convexity ranks in higher dimensions
A subset of a vector space is called countably convex if it is a countable union of convex sets. Classification of countably convex subsets of topological vector spaces is addressed in this paper. An ordinal-valued rank function ϱ is introduced to measure the complexity of local nonconvexity points in subsets of topological vector spaces. Then ϱ is used to give a necessary and sufficient condition for countable convexity of closed sets. Theorem. Suppose that S is a closed subset of a Polish linear...
Correct Soltan-Vasiloi criterion for convex cones.
Correction to the paper: Sets invariant under projections onto one dimensional subspaces
Countably convex sets
We investigate countably convex subsets of Banach spaces. A subset of a linear space is countably convex if it can be represented as a countable union of convex sets. A known sufficient condition for countable convexity of an arbitrary subset of a separable normed space is that it does not contain a semi-clique [9]. A semi-clique in a set S is a subset P ⊆ S so that for every x ∈ P and open neighborhood u of x there exists a finite set X ⊆ P ∩ u such that conv(X) ⊈ S. For closed sets this condition...