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

Document Type : Research Paper


1 Faculty of Mathematics, \Alexandru Ioan Cuza" University of Iasi Iasi, Romania

2 Department of Physics, Gheorghe Asachi Technical University of Iasi, Iasi, Romania


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


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