Convex Hilbert cubes in superextensions
Let X be a metrizable continuum. The superextension \(\lambda\) X of X is the space of all maximal linked systems of closed subsets of X equipped with a natural Wallman topology. It is known that \(\lambda\) X is homeomorphic to the Hilbert cube [see \textit{J. van Mill}, Fundam. Math. 107, 201-224 (1980; Zbl 0449.54024)]. Superextensions carry a natural convex structure. The author proves that each nondegenerate compact convex subset of \(\lambda\) X is homeomorphic to the Hilbert cube, thereby extending the reviewer's result in a nontrivial way.
maximal linked systems of closed subsets
scientific article; zbMATH DE number 3944814
scientific article