Constructing universally small subsets of a given packing index in Polish groups

Taras Banakh, and Nadya Lyaskovska. "Constructing universally small subsets of a given packing index in Polish groups." Colloquium Mathematicae 125.2 (2011): 213-220. <http://eudml.org/doc/283614>.

@article{TarasBanakh2011,
abstract = {A subset of a Polish space X is called universally small if it belongs to each ccc σ-ideal with Borel base on X. Under CH in each uncountable Abelian Polish group G we construct a universally small subset A₀ ⊂ G such that |A₀ ∩ gA₀| = for each g ∈ G. For each cardinal number κ ∈ [5,⁺] the set A₀ contains a universally small subset A of G with sharp packing index $pack♯(A_κ) = sup\{||⁺: ⊂ \{gA\}_\{g∈ G\} is disjoint\}$ equal to κ.},
author = {Taras Banakh, Nadya Lyaskovska},
journal = {Colloquium Mathematicae},
keywords = {universally small set; universally meager set; universally null set; packing index; Polish group; coanalytic set},
language = {eng},
number = {2},
pages = {213-220},
title = {Constructing universally small subsets of a given packing index in Polish groups},
url = {http://eudml.org/doc/283614},
volume = {125},
year = {2011},
}

TY - JOUR
AU - Taras Banakh
AU - Nadya Lyaskovska
TI - Constructing universally small subsets of a given packing index in Polish groups
JO - Colloquium Mathematicae
PY - 2011
VL - 125
IS - 2
SP - 213
EP - 220
AB - A subset of a Polish space X is called universally small if it belongs to each ccc σ-ideal with Borel base on X. Under CH in each uncountable Abelian Polish group G we construct a universally small subset A₀ ⊂ G such that |A₀ ∩ gA₀| = for each g ∈ G. For each cardinal number κ ∈ [5,⁺] the set A₀ contains a universally small subset A of G with sharp packing index $pack♯(A_κ) = sup{||⁺: ⊂ {gA}_{g∈ G} is disjoint}$ equal to κ.
LA - eng
KW - universally small set; universally meager set; universally null set; packing index; Polish group; coanalytic set
UR - http://eudml.org/doc/283614
ER -