On lower semicontinuous multifunctions in quasi-uniform and vector spaces

2002/04/10 by Andrzej Spakowski
Mathematics · #math.GN #msc:54C60 #msc:54E15 #msc:46A16

paper · pdf

published as Proceedings of the Ninth Prague Topological Symposium, (Prague, 2001), pp. 309--319, Topology Atlas, Toronto, 2002 · 11 pages

arxiv created 2002/04/10 · arxiv updated 2009/11/30

Abstract

Given a cover B of a quasi-uniform space Y we introduce a concept of lower semicontinuity for multifunctions F:X→ 2^Y, 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.

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