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Haar-I sets: Looking at small sets in Polish groups through compact glasses

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00546269" target="_blank" >RIV/67985840:_____/21:00546269 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.4064/dm812-2-2021" target="_blank" >http://dx.doi.org/10.4064/dm812-2-2021</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.4064/dm812-2-2021" target="_blank" >10.4064/dm812-2-2021</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Haar-I sets: Looking at small sets in Polish groups through compact glasses

  • Original language description

    Generalizing Christensen’s notion of a Haar-null set and Darji’s notion of a Haar-meager set, we introduce and study the notion of a Haar-I set in a Polish group. Here I is an ideal of subsets of some compact metrizable space K. A Borel subset B ⊆ X of a Polish group X is called Haar-I if there exists a continuous map f: K → X such that f−1 (B + x) ∈ I for all x ∈ X. Moreover, B is generically Haar-I if the set of witness functions {f ∈ C(K, X): ∀x ∈ X f−1 (B +x) ∈ I} is comeager in the function space C(K, X). We study (generically) Haar-I sets in Polish groups for many concrete and abstract ideals I, and construct the corresponding distinguishing examples. We prove some results on Borel hulls of Haar-I sets, generalizing results of Solecki, Elekes, Vidnyánszky, Doležal, Vlasák on Borel hulls of Haar-null and Haar-meager sets. We also establish various Steinhaus properties of the families of (generically) Haar-I sets in Polish groups for various ideals I.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2021

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Dissertationes Mathematicae

  • ISSN

    0012-3862

  • e-ISSN

    1730-6310

  • Volume of the periodical

    564

  • Issue of the periodical within the volume

    August

  • Country of publishing house

    PL - POLAND

  • Number of pages

    105

  • Pages from-to

    1-105

  • UT code for WoS article

    000697721200001

  • EID of the result in the Scopus database

    2-s2.0-85100276348