Abstract
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 and a metrisable topological vector space Z, the space M(X,Z) of minimal upper semi-continuous compact valued (musco) maps from X into 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 is a Baire space. We also study topologies of uniform convergence on compact sets on M(X,Z).
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