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

Abstract

n this paper, we consider continuity properties<br />(especially, regularity, also viewed as an approximation property) for $%<br />mathcal{P}_{0}(X)$-valued set multifunctions ($X$ being a linear,<br />topological space), in order to obtain Egoroff and Lusin type theorems for<br />set multifunctions in the Vietoris hypertopology. Some mathematical<br />applications are established and several physical implications of the<br />mathematical model of regularity are presented, which allows a<br />classification of the physical models.