On the geometric difference of multivalued mappings. (Q1809954)

The purpose of this paper is to prove some new continuity properties of the geometric difference of multivalued mappings with bounded values in separable Banach spaces. The finite-dimensional case is also considered. Actually, it is proved that in a separable Banach space endowed with the weak topology the geometric difference of an upper semicontinuous mapping and a lower semicontinuous one is upper semicontinuous, under some other additional assumptions. Then, in the finite-dimensional case, the continuity (with respect to the Hausdorff metric) for the geometric difference of two multifunctions (without the nonempty interior assumption) is established.