
Journal of Convex Analysis 27 (2020), No. 3, 10331049 Copyright Heldermann Verlag 2020 Convex Extension of Lower Semicontinuous Functions Defined on Normal Hausdorff Space Mohammed Bachir Laboratoire SAMM 4543, Université Panth\'eonSorbonne, 75634 Paris 13, France Mohammed.Bachir@univparis1.fr We prove that any problem of minimization of proper lower semicontinuous function defined on a normal Hausdorff space is canonically equivalent to a problem of minimization of a proper weakstar lower semicontinuous convex function defined on a weakstar convex compact subset of some dual Banach space. We establish the existence of a bijective operator between the two classes of functions which preserves problems of minimization. Keywords: Isomorphism, minimization problem, convex functions, normal Hausdorff space, the StoneCech compactification. MSC: 47N10, 46N10, 46E15. [ Fulltextpdf (148 KB)] for subscribers only. 