THE SPACE OF INFINITE-DIMENSIONAL COMPACTA AND OTHER TOPOLOGICAL COPIES OF {l})

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 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 is also homeomorphic to (lj) .