Erdős space and homeomorphism groups of manifolds / Jan J. Dijkstra, Jan van Mill

Bibliogr. p. 61-62

Let M be either a topological manifold, a Hilbert cube manifold, or a Menger manifold and let D be an arbitrary countable dense subset of M. Consider the topological group H(M,D) which consists of all autohomeomorphisms of M that map D onto itself equipped with the compact-open topology. The authors present a complete solution to the topological classification problem for H(M,D) as follows. If M is a one-dimensional topological manifold, then they proved in an earlier paper that H(M,D) is homeomorphic to Qω, the countable power of the space of rational numbers. In all other cases they find in this paper that H(M,D) is homeomorphic to the famed Erdős space E, which consists of the vectors in Hilbert space ℓ2 with rational coordinates. They obtain the second result by developing topological characterizations of Erdős space. (Source : AMS)