9 papers · 1 filter
Countable dense homogeneity in large products of Polish spaces
Andrea Medini, Juris Steprāns
We give a unified treatment of the countable dense homogeneity of products of Polish spaces, with a focus on uncountable products. Our main result states that a product of fewer th…
Countable dense homogeneity and topological groups
Claudio Agostini, Andrea Medini, Lyubomyr Zdomskyy
Building on results of Medvedev, we construct a example of a non-Polish topological group that is countable dense homogeneous. Our example is a dense subgroup of $\m…
On the infinite powers of large zero-dimensional metrizable spaces
Andrea Medini
We show that is strongly homogeneous whenever is a non-separable zero-dimensional metrizable space and is an infinite cardinal. This partially answers a question of T…
Every finite-dimensional analytic space is -homogeneous
Claudio Agostini, Andrea Medini
All spaces are assumed to be separable and metrizable. Building on work of van Engelen, Harrington, Michalewski and Ostrovsky, we obtain the following results: (1) Every finite-dim…
A complete classification of the zero-dimensional homogeneous spaces under determinacy
Andrea Medini
All spaces are assumed to be separable and metrizable. We give a complete classification of the zero-dimensional homogeneous spaces, under the Axiom of Determinacy. This classifica…
Countable spaces, realcompactness, and the pseudointersection number
Claudio Agostini, Andrea Medini, Lyubomyr Zdomskyy
All spaces are assumed to be Tychonoff. Given a realcompact space , we denote by the smallest infinite cardinal such that is homeomorphic to a closed s…