In this paper we revisit the question of when the continuous linear image of a fixed closed convex cone K is closed. Specifically, we improve the main result of [3] by showing that for all, except for at most a σ-porous set, of the linear mappings T from Rn into Rm, not only is T (K) closed, but there is also a neighbourhood around T whose members also preserve the closedness of K. AMS (2002) s...

In this paper, the characterization of closed and strongly closed subobjects of an object in categories of various types of filter convergence spaces is given and it is shown that they induce a notion of closure. Furthermore, each of the notions of compactness, perfectness, separation, minimality and absolute closedness with respect to these two new closure operators are characterized in these ...

We characterize in a reflexive Banach space all the closed convex sets containing no lines for which the condition ensures the closedness of the algebraic difference for all closed convex sets . We also answer a closely related problem: determine all the pairs , of closed convex sets containing no lines such that the algebraic difference of any sufficiently small uniform perturbation of and rem...

A mixture preorder is a on space (such as convex set) that compatible with the mixing operation. In decision theoretic terms, it satisfies central expected utility axiom of strong independence. We consider when has multi-representation consists real-valued, mixture-preserving functions. If does, must satisfy continuity Herstein and Milnor (1953). Mixture sufficient for dimension countable, but ...

In many areas of applied mathematics, decentralization information is a ubiquitous attribute affecting how to approach stochastic optimization, decision and estimation, or control problem. this review article, we present general formulation structures under probability theoretic geometric formulation. We define structures, place various topologies on them, study closedness, compactness convexit...

We propose a new class of stochastic integer programs whose special features are dominance constraints induced by mixed-integer linear recourse. For these models, we establish closedness of the constraint set mapping with the underlying probability measure as parameter. In the case of finite probability spaces, the models are shown to be equivalent to large-scale, block-structured, mixedinteger...

Multi-species reaction-diffusion systems, with more-than-two-site interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for Ea n (t)’s, the expectation value of the product of certain linear combination of the number operators on n consecutive sites at time...

For a contingent differential equation that takes values in the closed, convex, nonempty subsets of a Banach space E, we prove an existence theorem and we investigate the extendability of solutions and the closedness and continuity properties of solution funnels. We consider first a space E that is separable and reflexive and then a space E with a separable second dual space. We also consider t...

In this paper, we study generalized quasi-variational relation problems in locally G-convex spaces. Using the Kakutani-Fan-Glicksberg fixed-point theorem for upper semicontinuous set-valued mapping with nonempty closed acyclic values, we establish an existence theorem of a solution set for these problems. Moreover, the stability and closedness of the solution set for these problems are also obt...

We study the superreplication of contingent claims under model uncertainty in discrete time. We show that optimal superreplicating strategies exist in a general measure-theoretic setting; moreover, we characterize the minimal superreplication price as the supremum over all continuous linear pricing functionals on a suitable Banach space. The main ingredient is a closedness result for the set of...