On lower semicontinuous multifunctions in quasi-uniform and vector spaces

Details On lower semicontinuous multifunctions in quasi-uniform and vector spaces On lower semicontinuous multifunctions in quasi-uniform and vector spaces

2002-04-10

arxiv.org/abs/math/0204142v1

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

Mathematics

General Topology

11 pages

Scientific paper

Given a cover $\mathcal{B}$ of a quasi-uniform space $Y$ we introduce a concept of lower semicontinuity for multifunctions $F:X\to 2^Y$, called $\mathcal{B}$-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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