Alexandroff Theorem in Hausdorff Topology for Null-null-additive Set Multifunctions

In this paper we further a previous study concerning abstract regularity for monotone set multifunctions, with has immediate applications in well-known situations such as the Borel σ-algebra of a Hausdorff space and/or the Borel (Baire, respectively) δ-ring or σ-ring of a locally compact Hausdorff space. We also study relationships among abstract regularities and other properties of continuity. Especially, a set-valued Alexandroff type theorem is obtained. Mathematics Subject Classification 2010: 28B20, 28C15.