The space of infinite-dimensional compacta and other topological copies of (<i>l</i>_<i>f</i>²)^<i>ω</i>

Abstract

We show that there exists a homeomorphism from the hyperspace of the Hubert cube Q onto the countable product of Hubert cubes such that the > A:-dimensional sets are mapped onto B k x Q x Q x , where B is the pseudoboundary of Q. In particular, the infinitedimensional compacta are mapped onto B , which is homeomorphic to the countably infinite product of lj. In addition, we prove for k G {1,2,... ,00} that the space of uniformly > A-dimensional sets in 2 Q is also homeomorphic to (lj) .