On topological properties of the set of solutions of operator inclusions with a multi-valued Lipschitz right-hand side

This paper is devoted to the study of the topological dimension of the set of solutions of the operator inclusion of the form $A(x)\in\lambda F(x)$, where $A$ is a bounded linear surjective operator, and $F$ is a multi-valued Lipschitz map with closed convex images. The resulting theorem establishes a connection between the dimension of the kernel of the operator $A$ and the dimension of the set of solutions of this inclusion.