A general nonseparable theory of functions and multifunctions (Q1071340)

The paper presents an abstract approach to the study of multifunctions. The notions of measurability and continuity are very abstract to get them as general extensions of known results on continuity and measurability of multifunctions. The results apply also to the nonseparable range. Besides the generalization of known results also several new resuls on representation, interposition and extension are presented. The solution of problems of K. Kuratowski and A. H. Stone regarding the invariance of separability and absolutely Borel sets is announced but the corresponding theorems are rather reformulations of those problems. For example, Theorem 11.1 claims that the map f from a separable metric space X onto a metrizable space Y has a separable range iff there is some topology t on X with countable (\(\sigma\)-locally finite) base such that f:(X,t)\(\to Y\) is continuous. The results are stated without proofs and no paper with corresponding proofs is quoted.