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Currently displaying 1 – 2 of 2

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Constructing subsets of a given packing index in Abelian groups

Nadya Lyaskovska — 2007

Acta Universitatis Carolinae. Mathematica et Physica

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

Taras Banakh; Nadya Lyaskovska — 2011

Colloquium Mathematicae

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 $p a c k ♯ (A_{κ}) = s u p | | ⁺ : \subset {g A}_{g \in G} i s d i s j o i n t$ equal to κ.

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