  It is known that there are complete, Hausdorff and regular convergence vector
spaces X and Y such that Lc(X,Y), the space of continuous linear mappings from
X into Y equipped with the continuous convergence structure, is not complete.
In this paper, we give sufficient conditions on a convergence vector space Y
such that Cc(X,Y) is complete for any convergence space X. In particular, we
show that this is true for every complete and Hausdorff topological vector
space Y.
