On lower semicontinuous multifunctions in quasi-uniform and vector spaces

الأصل · EN

Given a cover B of a quasi-uniform space Y we introduce a concept of lower semicontinuity for multifunctions F:X→ 2ʸ, called B-lsc. In this way, we get a common description of Vietoris-lsc, Hausdorff-lsc, and bounded-Hausdorff-lsc as well. Further, we examine set-theoretical and vector operations on such multifunctions. We also point out that the convex hull of Hausdorff-lsc multifunctions need not to be Hausdorff-lsc except the case where the range space is locally convex.