On lower semicontinuous multifunctions in quasi-uniform and vector spaces

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dc.creatorSpakowski, Andrzej
dc.date2002-04-10
dc.date.accessioned2026-07-07T04:47:37Z
dc.date.available2026-07-07T04:47:37Z
dc.descriptionGiven 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.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/math/0204142
dc.identifierhttp://arxiv.org/abs/math/0204142
dc.identifierProceedings of the Ninth Prague Topological Symposium, (Prague, 2001), pp. 309--319, Topology Atlas, Toronto, 2002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63785
dc.subjectGeneral Topology
dc.subject54C60, 54E15, 46A16
dc.titleOn lower semicontinuous multifunctions in quasi-uniform and vector spaces
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