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A characterization of closed convex sets possessing a barrier cone with a nonempty interior is achieved. As a consequence, we describe all the proper extended-valued functionals for which the domain of their Fenchel conjugate has a nonempty interior. We end up the paper by giving an application to the study of the stability of the solution set of a(More)
We characterize in a reflexive Banach space all the closed convex sets 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 ¢ ¡(More)
The concept of continuous set has been used in finite dimension by Gale and Klee and recently by Auslender and Coutat. Here, we introduce the notion of slice-continuous set in a general reflexive Ba-nach space and we show that the class of such sets can be viewed as a subclass of the class of continuous sets. Further, we prove that every non constant(More)
This paper is devoted to studying boundedness criteria for extended-real-valued functions. The study is done in the framework of dual vector spaces, using new objects such as self-equilibrated sets and functions. We establish two boundedness new major criteria. The first one says that an extended-real-valued function is bounded below provided it is(More)