In this paper we present a theorem for defining fixed-points in categories of sheaves. This result gives a unifying and general account of most techniques used in computer science in order to ensure convergency of circular definitions, such as (but not limited to) well-founded recursion and contractivity in complete ultra metric spaces. This general fixed-point theorem encompasses also a simila...

Egoroff’s theorem is established for set-valued measures, which take values in the family of all non-void, closed subsets of a real normed space using Hausdorff metric by several authors. In this paper, we prove Egoroff’s theorem remains valid for non-additive measures, which take values in a family of sets of topological vector spaces using two types of convergency of set sequences.