Functor of completed iterated inclusion hyperspace
Let X be a metrizable continuum; then \(\tilde{\tilde G}(X)\) denotes the completion of the iterated inclusion hyperspace \(\tilde G(X)\) (as a direct limit in the category of metric spaces and isometric embeddings), and \(\bar G(X)\) denotes the compactification of \(\tilde{\tilde G}(X)\). The author proves that for any nondegenerated metrizable continuum X, the pair \((\bar G(X),\tilde{\tilde G}(X))\) is homeomorphic to (Q,s), where s is the pseudo-interior of the Hilbert cube. The proof of the theorem uses the technique of Z-skeletoids by \textit{C. Bessaga} and \textit{A. Pelczyński}. The other methods used are quite standard, nevertheless the obtained result is considerably interesting.
scientific article; zbMATH DE number 4180297