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 equal to κ.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-2-6,
author = {Taras Banakh and Nadya Lyaskovska},
title = {Constructing universally small subsets of a given packing index in Polish groups},
journal = {Colloquium Mathematicae},
volume = {122},
year = {2011},
pages = {213-220-},
zbl = {1258.03060},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-2-6}
}
Taras Banakh; Nadya Lyaskovska. Constructing universally small subsets of a given packing index in Polish groups. Colloquium Mathematicae, Tome 122 (2011) . http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-2-6/