We exhibit a simple topology on the closed convex subsets C of a normed linear space such that, under the usual ways of combining convex sets, C becomes a topological algebra. The topolog is the weakest one on C for which distance and support functionals are both continuous, as functions of the set argument. This topology is also the weakest topology for whichandis a continuous function on. e×e In a reflexive space, convergence of asequence in C with respect to this topology is equivalent to pointwise plus Mosco convergence of the corresponding sequence of support functionals