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
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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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