Linear and quasi-linear spaces of set-valued maps
In this paper we investigate the algebraic structure of certain spaces of set-valued maps. Among other results, we show that for an arbitrary topological space X X and a metrisable topological vector space Z Z , the space M(X,Z) M ( X , Z ) of minimal upper semi-continuous compact valued (musco) maps from X X into Z Z is a linear space. This result extends a previously known result on the linear structure of spaces of musco maps. Previously, this result was known only in the case when X X is a Baire space. We also study topologies of uniform convergence on compact sets on M(X,Z) M ( X , Z ) .
linear space set-valued maps compact-open topology