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… (More)

If X is a topological space, then we let H(X) denote the group of autohomeomorphisms of X equipped with the compact-open topology. For subsets A and B of X we define [A, B] = {h ∈ H(X) : h(A) ⊂ B},… (More)

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… (More)

We show that for every p > 0 there is an autohomeomor-phism h of the countable innnite product of lines R N such that for every r > 0, h maps the Hilbert cube ?r; r] N precisely onto the \ellip-tic… (More)

In this paper we primarily consider two natural subgroups of the autohomeomorphism group of the real line R, endowed with the compact-open topology. First, we prove that the subgroup of… (More)

In 1940 Paul Erdős introduced the ‘rational Hilbert space’, which consists of all vectors in the real Hilbert space 2 that have only rational coordinates. He showed that this space has topological… (More)

The space now known as complete Erdős space Ec was introduced by Paul Erdős in 1940 as the closed subspace of the Hilbert space l2 consisting of all vectors such that every coordinate is in the… (More)

It is shown that the homeomorphism groups of the (generalized) Sierpiński carpet and the universal Menger continua are not zero-dimensional. These results were corollaries to a 1966 theorem of… (More)

We announce a complete topological classification of the function spaces C (X) of Borel class not higher than 2, provided that I is a countable space. We also present a topological classification of… (More)