On the Main Theorems of Superconvex Analysis

Abstract

The present paper is devoted to the theory of superconvex spaces as developed over the past twelve years in the circle of the author in Saarbrucken; in particular fundamental contributions are due to Gerd Rode and Norbert Kuhn. The paper is a sequel to [2] and [3]; we also mention [1] as a report from the old times. We propose to present the core of the theory in a new shape: the main theorems in some new versions which are simpler and easier to formulate, with much shorter proofs and clearer realization of their mutual dependence. The basic observation is the short route from the intersection theorem [2] Theorem 2.1 (= Theorem 1 below) to the basic estimation (Theorem 2 below) which is to replace [3] Theorem 4.3. For the sake of completeness we also include a few proofs which are not much different from the earlier ones.