Topology Atlas
Document # ppae-28

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

### Andrzej Spakowski

Proceedings of the Ninth Prague Topological Symposium
(2001)
pp. 309-319
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.

Mathematics Subject Classification. 54C60 54E15 46A16.

Keywords. Lower semicontinuous multifunctions (set-valued maps), cartesian
product, intersection, vector sum, and convex hull of multifunctions..

- Document formats
- AtlasImage (for online previewing)
- LaTeX
`34.7 Kb`
- DVI
`54.7 Kb`
- PostScript
`199.8 Kb`
- gzipped PostScript
`77.0 Kb`
- PDF
`205.1 Kb`
- arXiv
- math.GN/0204142
- Metadata
- Citation
- Reference list in BibTeX

Comments. This article is in final form.

Copyright © 2002
Charles University and
Topology Atlas.
Published April 2002.