Selections and Continuity-Like Set-Valued Mappings
by
Valentin G. Gutev
University of Sofia

As a rule, the selection theorems for l.s.c. mappings characterize some separation properties (like paracompactness , collectionwise normality , normality , etc.) of the domain of these mappings. In contrary to this, certain selection theorems which are known for l.s.c. mappings with paracompact (or similar) domain are also true for continuity-like set-valued mappings with arbitrary domain. Such an exchange fits naturally into the selection theory showing that several known selection theorems for ``continuous'' set-valued mappings remain true under minimal hypotheses as well as it is very useful in proving new selection results for spaces of closed subsets.

Date received: July 22, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caaj-49.