Radial continuity of set-valued metric projections

Lower Semicontinuity Concepts, Continuous Selections, and Set Valued Metric Projections

A number of semicontinuity concepts and the relations between them are discussed. Characterizations are given for when the (set-valued) metric projection P M onto a proximinal subspace M of a normed linear space X is approximate lower semicontinuous or 2-lower semicontinuous. A geometric characterization is given of those normed linear spaces X such that the metric projection onto every one-dim...

Some New Continuity Concepts for Metric Projections

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...

Semi-continuity of Metric Projections in ∞-direct Sums

Let Y be a proximinal subspace of finite codimension of c0. We show that Y is proximinal in ∞ and the metric projection from ∞ onto Y is Hausdorff metric continuous. In particular, this implies that the metric projection from ∞ onto Y is both lower Hausdorff semi-continuous and upper Hausdorff semi-continuous.

Continuity Properties of Convex-type Set-valued Maps

K–convex, K–midconvex and (K,λ)–convex set–valued maps are considered. Several conditions implying the continuity of such maps are collected.