Andrea Medini

activity

20092026

most citedSeven characterizations of non-meager P-filters

6 citations · 18 across the 19 of their papers we have counts for

collaborators

25 papers

math.LO2026

Non-meager $P$ -filters, Miller-measurability, and a question of Hrušák

Andrea Medini

Given a cardinal $κ$ and filters $F_{α}$ on $ω$ for $α \in κ$ , we will show that if $\prod_{α \in κ} F_{α}$ is countable dense homogeneous then $κ < p$ and each…

math.GN2025

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…

math.GN2025

Countable dense homogeneity and topological groups

Claudio Agostini, Andrea Medini, Lyubomyr Zdomskyy

Building on results of Medvedev, we construct a $ZFC$ example of a non-Polish topological group that is countable dense homogeneous. Our example is a dense subgroup of $\m…

math.GN2025

On the infinite powers of large zero-dimensional metrizable spaces

Andrea Medini

We show that $X^{λ}$ is strongly homogeneous whenever $X$ is a non-separable zero-dimensional metrizable space and $λ$ is an infinite cardinal. This partially answers a question of T…

math.GN2024

Every finite-dimensional analytic space is $σ$ -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…

math.GN2023

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…

math.GN2023

Countable spaces, realcompactness, and the pseudointersection number

Claudio Agostini, Andrea Medini, Lyubomyr Zdomskyy

All spaces are assumed to be Tychonoff. Given a realcompact space $X$ , we denote by $Exp (X)$ the smallest infinite cardinal $κ$ such that $X$ is homeomorphic to a closed s…

math.GN2021

On the scope of the Effros theorem

Andrea Medini

All spaces (and groups) are assumed to be separable and metrizable. Jan van Mill showed that every analytic group $G$ is Effros (that is, every continuous transitive action of $G$ …

math.GN2021

Zero-dimensional $σ$ -homogeneous spaces

Andrea Medini, Zoltán Vidnyánszky

All spaces are assumed to be separable and metrizable. Ostrovsky showed that every zero-dimensional Borel space is $σ$ -homogeneous. Inspired by this theorem, we obtain the followin…

math.LO2019

Constructing Wadge classes

Raphaël Carroy, Andrea Medini, Sandra Müller

We show that, assuming the Axiom of Determinacy, every non-selfdual Wadge class can be constructed by starting with those of level $ω_{1}$ (that is, the ones that are closed under Bo…

math.GN2018

Every zero-dimensional homogeneous space is strongly homogeneous under determinacy

Raphaël Carroy, Andrea Medini, Sandra Müller

All spaces are assumed to be separable and metrizable. We show that, assuming the Axiom of Determinacy, every zero-dimensional homogeneous space is strongly homogeneous (that is, a…

math.GN2017★ 3 cited

Infinite powers and Cohen reals

Andrea Medini, Jan van Mill, Lyubomyr Zdomskyy

We give a consistent example of a zero-dimensional separable metrizable space $Z$ such that every homeomorphism of $Z^{ω}$ acts like a permutation of the coordinates almost everywher…

math.GN2016★ 2 cited

On Borel semifilters

Andrea Medini

Building on work of van Engelen and van Mill, we show that a zero-dimensional Borel space is homeomorphic to a semifilter if and only if it is homogeneous and not locally compact.…

math.GN2016

Every filter is homeomorphic to its square

Andrea Medini, Lyubomyr Zdomskyy

We show that every filter $F$ on $ω$ , viewed as a subspace of $2^{ω}$ , is homeomorphic to $F^{2}$ . This generalizes a theorem of van Engelen, who proved that this h…

math.GN2015★ 2 cited

Non-meager free sets and independent families

Andrea Medini, Dušan Repovš, Lyubomyr Zdomskyy

Our main result is that, given a collection $R$ of meager relations on a Polish space $X$ such that $∣ R ∣ \leq ω$ , there exists a dense Baire subspace $F$ of $X$ (…

math.GN2014

A homogeneous space whose complement is rigid

Andrea Medini, Jan van Mill, Lyubomyr Zdomskyy

We construct a homogeneous subspace of $2^{ω}$ whose complement is dense in $2^{ω}$ and rigid. Using the same method, assuming Martin's Axiom, we also construct a countable dense homog…

math.GN2014

Countable dense homogeneity in powers of zero-dimensional definable spaces

Andrea Medini

We show that, for a coanalytic subspace $X$ of $2^{ω}$ , the countable dense homogeneity of $X^{ω}$ is equivalent to $X$ being Polish. This strengthens a result of Hrušák and Zamora Avi…

math.GN2014

Between Polish and completely Baire

Andrea Medini, Lyubomyr Zdomskyy

All spaces are assumed to be separable and metrizable. Consider the following properties of a space $X$ . (1) $X$ is Polish. (2) For every countable crowded $Q \subseteq X$ there exi…

math.GN2014

Productively Lindelöf spaces of countable tightness

Andrea Medini, Lyubomyr Zdomskyy

Michael asked whether every productively Lindelöf space is powerfully Lindelöf. Building of work of Alster and De la Vega, assuming the Continuum Hypothesis, we show that every pro…

math.LO2014

Distinguishing perfect set properties in separable metrizable spaces

Andrea Medini

All spaces are assumed to be separable and metrizable. Our main result is that the statement "For every space $X$ , every closed subset of $X$ has the perfect set property if and on…

math.GN2013★ 6 cited

Seven characterizations of non-meager P-filters

Kenneth Kunen, Andrea Medini, Lyubomyr Zdomskyy

We give several topological/combinatorial conditions that, for a filter on $ω$ , are equivalent to being a non-meager $P$ -filter. In particular, we show that a filter is co…

math.GN2013★ 5 cited

Products and countable dense homogeneity

Andrea Medini

Building on work of Baldwin and Beaudoin, assuming Martin's Axiom, we construct a zero-dimensional separable metrizable space $X$ such that $X$ is countable dense homogeneous while…

math.GN2011

The topology of ultrafilters as subspaces of $2^{ω}$

Andrea Medini, David Milovich

Using the property of being completely Baire, countable dense homogeneity and the perfect set property we will be able, under Martin's Axiom for countable posets, to distinguish no…

math.GN2010

A non-CLP-compact product space whose finite subproducts are CLP-compact

Andrea Medini

We construct a family of Hausdorff spaces such that every finite product of spaces in the family (possibly with repetitions) is CLP-compact, while the product of all spaces in the…

Non-meager P-filters, Miller-measurability, and a question of Hrušák

Countable dense homogeneity in large products of Polish spaces

Countable dense homogeneity and topological groups

On the infinite powers of large zero-dimensional metrizable spaces

Every finite-dimensional analytic space is σ-homogeneous

A complete classification of the zero-dimensional homogeneous spaces under determinacy

Countable spaces, realcompactness, and the pseudointersection number

On the scope of the Effros theorem

Zero-dimensional σ-homogeneous spaces

Constructing Wadge classes

Every zero-dimensional homogeneous space is strongly homogeneous under determinacy

Infinite powers and Cohen reals

On Borel semifilters

Every filter is homeomorphic to its square

Non-meager free sets and independent families

A homogeneous space whose complement is rigid

Countable dense homogeneity in powers of zero-dimensional definable spaces

Between Polish and completely Baire

Productively Lindelöf spaces of countable tightness

Distinguishing perfect set properties in separable metrizable spaces

Seven characterizations of non-meager P-filters

Products and countable dense homogeneity

The topology of ultrafilters as subspaces of 2ω

A non-CLP-compact product space whose finite subproducts are CLP-compact

Non-meager $P$ -filters, Miller-measurability, and a question of Hrušák

Every finite-dimensional analytic space is $σ$ -homogeneous

Zero-dimensional $σ$ -homogeneous spaces

The topology of ultrafilters as subspaces of $2^{ω}$