Preface. 1. Preliminaries. 2. Weak Topologies determined by Distance Functionals. 3. The Attouch--Wets and Hausdorff Metric Topologies. 4. Gap and Excess Functionals and Weak Topologies. 5. The Fell… Expand

Let CL(X) denote the nonempty closed subsets of a metrizable space X. We show that the Vietoris topology on CL(X) is the weakest topology on CL(X) such that A -→ d(x, A) is continuous for each x ε X… Expand

It is shown, subject to some standard constraint qualifications, that the operations of addition and restriction are continuous and are applied to convex well-posed optimization problems, as well as to convergence of approximated solutions in infinite dimensional convex programming.Expand

Let (X, d) be a complete and separable metric space. The Wijsman topology on the nonempty closed subset CL(X) of X is the weakest topology on CL(X) such that for each x in X, the distance functional… Expand

Atsuji has internally characterized those metric spaces X for which each real-valued continuous function on X is uniformly continuous as follows: (1) the set X' of limit points of X is compact, and… Expand

Let P be a right rectangular parallelepiped in R and let Y be a metric space. If Γ:P->Y is an upper semicontinuous multifunction such that for each x in P the set Γ(x) is nonempty and closed, then… Expand

A net 〈Aλ〉 of nonempty closed sets in a metric space 〈X, d〉 is declaredWijsman convergent to a nonempty closed setA provided for eachx εX, we haved(x, A)=limλd(x, A). Interest in this convergence… Expand