The space of infinite-dimensional compacta and other topological copies of (l_f²)^ω

Jan Dijkstra, Jan van Mill and Jerzy Mogilski

Vol. 152 (1992), No. 2, 255–273

DOI: 10.2140/pjm.1992.152.255

Abstract

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 ≥ k-dimensional sets are mapped onto B^k × Q × Q ×⋯ , where B is the pseudoboundary of Q. In particular, the infinite-dimensional compacta are mapped onto B^ω, which is homeomorphic to the countably infinite product of l_f². In addition, we prove for k ∈{1,2,…,∞} that the space of uniformly ≥ k-dimensional sets in 2^Q is also homeomorphic to (l_f²)^ω.

Mathematical Subject Classification 2000

Primary: 57N20

Secondary: 54H99

Milestones

Received: 15 April 1990

Revised: 3 May 1991

Published: 1 February 1992