Functor of completed iterated inclusion hyperspace
type: Item
instance of: scholarly article
title: Functor of completed iterated inclusion hyperspace
zbMATH Open document ID: 0716.54007
author: R. E. Mirzakhanyan
published in: Moscow University Mathematics Bulletin
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54B30
zbMATH DE Number: 4180297
zbMATH Keywords: metrizable continuum
zbMATH Keywords: iterated inclusion hyperspace
reviewed by: Jiri Vinarek
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4180297