CHAPTER 16 Continuous Selections of Multivalued Mappings Duˇ san Repovˇ s 1 Institute of Mathematics, Physics and Mechanics, University of Ljubljana Jadranska 19, P. O. Box 2964 Ljubljana, Slovenia 1001 E-mail: dusan.repovs@uni-lj.si Pavel V. Semenov 2 Department of Mathematics, Moscow City Pedagogical University 2nd Sel’skokhozyastvennyi pr.4, Moscow, Russia 129226 E-mail: pavels@orc.ru Contents 1. Solution of Michael’s problem for C-domains ............................. 425 2. Selectors for hyperspaces ........................................ 431 3. Relations between U- and L-theories .................................. 437 4. Miscellaneous results .......................................... 444 5. Open problems ............................................. 452 References ................................................. 456 1 Supported in part by the Ministry of Education, Science and Sport of the Republic of Slovenia research program No. 0101-509. 2 Supported in part by the RFBR research grant No. 02-01-00014. RECENT PROGRESS IN GENERAL TOPOLOGY II Edited by Miroslav Huˇ sek and Jan van Mill c 2002 Elsevier Science B.V. All rights reserved