P. Leonetti

works on

characterized subgroups 1 descriptive set theory 1 ideals 1 topological groups 1 unit circle 1

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math.GN2026

Complexity and Polishability of characterized subgroups on the unit circle

Paolo Leonetti

Given an ideal $I$ on $ω$ , a subgroup $H$ of the unit circle $T$ is said to be $I$ -characterized if there exists a sequence of integers $(a_{n} : n \in ω)$ such…

math.GN2026

Linear relations modulo meager sets

Marek Balcerzak, Paolo Leonetti

We prove several topological zero-one laws. First, we show that, if a subset $A$ of a Banach space $X$ has the Baire property, then $A$ admits a somewhere dense set of vectors $x \…

math.GN2026

On rough ideal convergence

Paolo Leonetti

We continue the study of ideal convergence for sequences $(x_{n})$ with values in a topological space $X$ with respect to a family ${F_{I^} \cdot : I^\cdot \in X}$ of subsets of $X$ with $Î·\in F_…

math.GN2026

Sets of Ramsey-limit points and IP-limit points

RafaÅ FilipÃ³w, Adam Kwela, Paolo Leonetti

Let $X$ be an uncountable Polish space and let $H$ be the Hindman ideal, that is, the family of all $S \subseteq I ¨ $ which are not $I P$ -sets. For each sequence $x=(x_n)_{n…

math.GN2025

On maldistributed sequences and meager ideals

Paolo Leonetti

We show that an ideal $I$ on $I ¨ $ is meager if and only if the set of sequences $(x_{n})$ taking values in a Polish space $X$ for which all elements of $X$ are $\mathcal{I}…

math.GN2025

Borel complexity of sets of ideal limit points

Rafal Filipow, Adam Kwela, Paolo Leonetti

Let $X$ be an uncountable Polish space and let $I$ be an ideal on $I ¨ $ . A point $I^\cdot \in X$ is an $I$ -limit point of a sequence $(x_{n})$ taking values in $X$ if th…