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...
Decompositions of compact convex sets.
Dilated Sets and Characterizations of Simplexes.
Distances to spaces of affine Baire-one functions
Let E be a Banach space and let and denote the space of all Baire-one and affine Baire-one functions on the dual unit ball , respectively. We show that there exists a separable L₁-predual E such that there is no quantitative relation between and , where f is an affine function on . If the Banach space E satisfies some additional assumption, we prove the existence of some such dependence.
Duality in vector optimization. II. Vector quasiconcave programming
Existence of open quasiconvex subsets dense in a given space
Extreme and exposed representing measures of the disk algebra
We study the extreme and exposed points of the convex set consisting of representing measures of the disk algebra, supported in the closed unit disk. A boundary point of this set is shown to be extreme (and even exposed) if its support inside the open unit disk consists of two points that do not lie on the same radius of the disk. If its support inside the unit disk consists of 3 or more points, it is very seldom an extreme point. We also give a necessary condition for extreme points to be exposed...