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The space of infinite-dimensional compacta and other topological copies of \((l_ f^ 2)^ \omega\). (English) Zbl 0786.54012
Summary: We show that there exists a homeomorphism from the hyperspace of the Hilbert cube \(Q\) onto the countable product of Hilbert cubes such that the \(\geq k\)-dimensional sets are mapped onto \(B^ k\times Q\times Q\times\cdots\), where \(B\) is the pseudoboundary of \(Q\). In particular, the infinite-dimensional compacta are mapped onto \(B^ \omega\), which is homeomorphic to the countably infinite product of \(l^ 2_ f\). In addition, we prove for \(k\in\{1,2,\dots,\infty\}\) that the space of uniformly \(\geq k\)-dimensional sets in \(2^ Q\) is also homeomorphic to \((l^ 2_ f)^ \omega\).

MSC:
54B20 Hyperspaces in general topology
54E45 Compact (locally compact) metric spaces
Keywords:
Hilbert cube
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