Approximation theorems for fuzzy set multifunctions in Vietoris topology. Physical implications of regularity

n this paper, we consider continuity properties(especially, regularity, also viewed as an approximation property) for %mathcal{P}_{۰}(X)-valued set multifunctions (X being a linear,topological space), in order to obtain Egoroff and Lusin type theorems forset multifunctions in the Vietoris hypertopology. Some mathematicalapplications are established and several physical implications of themathematical model of regularity are presented, which allows aclassification of the physical models.

Keywords:

Vietoris topology , Regularity , Approximations , Fractal Theories , Non-differentiable physics , Scale relativity theory