A closed epigraph theorem

Abstract

1. Various generalizations of the notion of convexity are known in the literature. One of them is the notion of d-convexity or convexity in Meng er s sense (M-convexity) in a metric space (X,d) (cf. H. Busemann L1J, B«TI« Cojush [2], Menger [8], E91). We shall confine ourselves to the notion of convexity in the so called G-space. In papers of B»n» Cojitsh C2]-[SJ and J. Ger C6] the notion of convex function defined on a metric space was introduced. Below we recall those properties of G-spaces which will be useful in the sequel referring to Ql] for further details (Fragment tekstu).