Hyperspace of max-plus convex compact sets
L. E. Bazilevich · Mathematical Notes · 2008
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 homeomorphic to $$ I^{\omega _1 } $$ .