Minimal Usco and Minimal Cusco Maps

Document Type : Original Article


1 Academy of Sciences, Institute of Mathematics Stefˇ anikova 49, 81473 Bratislava,´ Slovakia

2 Department of Mathematics and Computer Science, Faculty of Education, Trnava University, Priemyselna 4, 918 43 Trnava, Slovakia´


The main aim of this paper is to present a survey of known results concerning minimal usco and minimal cusco maps. We give characterizations of minimal usco and minimal cusco maps in the class of all set-valued maps using quasicontinuous selections. If X is a topological space and Y is a Banach space,  there is a bijection  between the space of minimal usco maps from X to Y and the space of minimal cusco maps from X to Y. We study this bijection with respect to various topologies on underlying spaces. Some new results are also given.


Main Subjects