  A convergence structure generalizing the order convergence structure on the
set of Hausdorff continuous interval functions is defined on the set of minimal
usco maps. The properties of the obtained convergence space are investigated
and essential links with the pointwise convergence and the order convergence
are revealed. The convergence structure can be extended to a uniform
convergence structure so that the convergence space is complete. The important
issue of the denseness of the subset of all continuous functions is also
addressed.
