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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
Hilbert cube
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