A Rogalski-Cornet Type Inclusion Theorem Based on Two Hausdorff Locally Convex Vector Spaces

Abstract

A Rogalski-Cornet type inclusion theorem based on two Hausdorff locally convex vector spaces is proved and composed of two parts. An example is presented to show that the associated set-valued map in the first part does not need any conventional continuity conditions including upper hemicontinuous. As an application, solvability results regarding an abstract von Neumann inclusion system are obtained.