On the hyperspace of max-min convex compact sets - Bazylevych, L. E. (Methods of Functional Analysis and Topology, 2009)
A subset A of R^n is said to be max-min convex if, for any x,yA and any tR, we have xtyA (here stands for the coordinatewise maximum of two elements in R^n and t(y_1,…,y_n)=({t,y_1},…, {t,y_n})). It is proved that the hyperspace of compact max-min convex sets in the Euclidean space R^n, n2, is homeomorphic to the punctured Hilbert cube. This is a counterpart of the result by Nadler, Quinn and Stavrokas proved for the hyperspace of compact convex sets. We also investigate the maps of the hyperspaces of compact max-min convex sets induced by the projection maps of Euclidean spaces. It is proved that this map is a Hilbert cube manifold bundle.