Hyperspace of Max-Plus Convex Compact Sets

The hyperspace mpcc(R(n)) of max-plus convex compact subsets of R(n), n >= 2, is considered. The main result is as follows: this hyperspace is a contractible manifold modeled on the Hilbert cube Q. It is also shown that the projection mapping mpcc(R(n)) --> mpcc(R(m)), n >= m is open. Moreover, it is proved that the hyperspace mpcc(I(omega 1)) of the Tikhonov [Tychonoff] cube I(omega 1) is homeornorphic to I(omega 1).