Generic continuity of minimal set-valued mappings

Continuity notions for multi-valued mappings

If we regard a multi-valued mapping as a generalization of a single-valued mapping, we may ask for generalizations of important properties as well, concerning fixed-points, projection, composition etc. The main interest in this paper are continuity notions for multi-valued mappings which allow non-connected images, but still have a certain fixed-point property. The starting point is a continuit...

Discrete Set-Valued Continuity and Interpolation

The main question of this talk is to retrieve some continuity properties on (discrete) T0-Alexandroff spaces. One possible application, which will guide us, is the construction of the so-called "tree of shapes" (intuitively, the tree of level lines). This tree, which should allow to process in the same way maxima and minima, faces quite a number of theoretical difficulties that we propose to so...

Weighted Variational Inequalities with Set-valued Mappings

Because of their applications in economics, game theory, mathematical physics, operations research and other areas, many classes of vector variational inequalities were intensively studied. For existence of solutions, resolution methods or equivalence with equilibrium and optimization problems see, for example, [11], [14], [15], [19], [17] and the references therein. For the study of variationa...

A Sard Theorem for Set-Valued Mappings∗†

If F is a set-valued mapping from IRn into IRm with closed graph, then y ∈ IRm is a critical value of F if for some x with y ∈ F (x), F is not metrically regular at (x, y). We prove that the set of critical values of a set-valued mapping whose graph is a definable (tame) set in an o-minimal structure containing additions and multiplications is a set of dimension not greater than m − 1 (resp. a ...

Fixed Point Theorems for Set-valued Mappings