Let W be an arbitrary subset of IR and posW the positive hull of W . We are concerned with conditions under which one can guarantee continuity properties for posW as a function of W . The results are then applied in the context of semi-infinite linear programs and stochastic programs with recourse.

The purpose of this note is to make a comment bearing upon the remarkable results of Radó on the semi-continuity of double integrals in parametric form. The essence of the situation, without at first attempting precision, is this. A continuous surface is of class K\ if and only if it has a representation for which the classical double integral area formula has meaning. (It is understood that th...

We prove two relative local variational principles of topological pressure functions P (T,F ,U , y) and P (T,F ,U|Y ) for a given factor map π, an open cover U and a subadditive sequence of real-valued continuous functions F . By proving the upper semi-continuity and affinity of the entropy maps h{·}(T,U | Y ) and h+{·}(T,U | Y ) on the space of all invariant Borel probability measures, we show...

In this note we show that in a certain subfamily of the Kuranishi family of any half Inoue surface the algebraic dimensions of the fibers jump downwards at special points of the parameter space showing that the upper semi-continuity of algebraic dimensions in any sense does not hold in general for families of compact non-Kähler manifolds. In the Kähler case, the upper semi-continuity always hol...

The relative entropy of entanglement $E_R$ is defined as the distance a multi-partite quantum state from set separable states measured by entropy. We show that this optimisation always achieved, i.e. any admits closest state, even in infinite dimensions; also, everywhere lower semi-continuous. use to derive dual variational expression for terms an external supremum instead infimum. These result...

Radzik (1991) showed that, by strengthening the usual quasi-concavity assumption on players’ payoff functions, upper semi-continuous two-player games on compact intervals of the real line have ε-equilibria for all ε > 0. Ziad (1997) then stated that the same conclusion holds for n-player games on compact, convex subsets of Rm, m ≥ 1, provided that the upper semi-continuity condition is strength...

Abstract. In this paper, we first derive specific results concerning the continuity and upper semi-continuity of the spectral radius and spectrum functions on fundamental locally multiplicative topological algebras. We continue our investigation by further determining the automatic continuity of linear mappings and homomorphisms in these algebras.