Topology via enriched categories

Having as a starting point the characterization of probabilistic metric spaces as enriched categories over the quantale , conditions that allow the generalization of results relating Cauchy sequences, convergence of sequences, adjunctions of V-distributors and its representability are established. Equivalence between L-completeness and L-injectivity is also established. L-completeness is characterized via the Yoneda embedding, and injectivity is related with exponentiability. Another kind of completeness is considered and the formal ball model is analyzed.

Implicit optimality criterion for convex SIP problem with box constrained index set

We consider a convex problem of Semi-Infinite Programming (SIP) with multidimensional index set. In study of this problem we apply the approach suggested in [20] for convex SIP problems with one-dimensional index sets and based on the notions of immobile indices and their immobility orders. For the problem under consideration we formulate optimality conditions that are explicit and have the form of criterion. We compare this criterion with other known optimality conditions for SIP and show its efficiency in the convex case.