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

• Autorzy: Taras Banakh , Nadya Lyaskovska
• Języki publikacji: EN

Abstrakty

EN

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| = 𝔠 for each g ∈ G. For each cardinal number κ ∈ [5,𝔠⁺] the set A₀ contains a universally small subset A of G with sharp packing index $pack♯(A_κ) = sup{|𝓓|⁺: 𝓓 ⊂ {gA}_{g∈ G} is disjoint}$ equal to κ.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 03E50: Continuum hypothesis and Martin's axiom
• 03E15: Descriptive set theory
• 22A05: Structure of general topological groups
• 54H11: Topological groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 125
• Numer: 2
• Strony: 213-220

Daty

wydano

2011

Twórcy

autor

Taras Banakh

• Institute of Mathematics, Jan Kochanowski University, Kielce, Poland
• Faculty of Mechanics and Mathematics, Ivan Franko National University of Lviv, 79000 Lviv, Ukraine

autor

Nadya Lyaskovska

• Faculty of Mechanics and Mathematics, Ivan Franko National University of Lviv, Universytetska 1, 79000 Lviv, Ukraine

Identyfikatory

DOI

10.4064/cm125-2-6