Jan J. Dijkstra

Complete Erdös space is unstable

It is proved that the countably infinite power of complete Erd˝ space Ec is not homeomorphic to Ec. The method by which this result is obtained consists of showing that Ec does not contain arbitrarily small closed subsets that are one-dimensional at every point. This observation also produces solutions to several problems that were posed by Aarts, Kawamura, Oversteegen and Tymchatyn. In addition, we show that the original (rational) Erd˝ os space does contain arbitrarily small closed sets that are

Function spaces of low Borel complexity

In this paper we investigate situations in which the space C,(X) of continuous, real-valued functions on X is a Borel subset of the product space RX. We show that for completely regular, nondiscrete spaces, C,7( X) cannot be a G8, an F, or a GR, subset of RX, but it can be an Fo& or Ga,,1& subset.

Homeomorphism groups of manifolds and Erdös space

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. We present a complete solution to the topological classification problem for H(M, D) as follows. If M is a one-dimensional topological manifold, then H(M, D) is homeomorphic to ℚ

A criterion for Erdös spaces

In 1940 Paul Erdős introduced the ‘rational Hilbert space’, which consists of all vectors in the real Hilbert space

On homeomorphism groups and the compact-open topology

\ell^2

On homeomorphism groups of Menger continua

that have only rational coordinates. He showed that this space has topological dimension one, yet it is totally disconnected and homeomorphic to its square. In this note we generalize the construction of this peculiar space and we consider all subspaces

Recent classification and characterization results in geometric topology

\mathcal{E}

Homogeneity properties with isometries and Lipschitz functions

of the Banach spaces

Classification of finite-dimensional universal pseudo-boundaries and pseudo-interiors

\ell^p

On the Group of Homeomorphisms of the Real Line That Map the Pseudoboundary Onto Itself

that are constructed as ‘products’ of zero-dimensional subsets