Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 50, Number 4 (2009), 453-468.
Packing Index of Subsets in Polish Groups
For a subset A of a Polish group G, we study the (almost) packing index pack( A) (respectively, Pack( A)) of A, equal to the supremum of cardinalities |S| of subsets such that the family of shifts is (almost) disjoint (in the sense that for any distinct points ). Subsets with small (almost) packing index are large in a geometric sense. We show that for any σ-compact subset A of a Polish group. In each nondiscrete Polish Abelian group G we construct two closed subsets with and and then apply this result to show that G contains a nowhere dense Haar null subset with pack(C)=Pack(C)=κ for any given cardinal number .
Notre Dame J. Formal Logic, Volume 50, Number 4 (2009), 453-468.
First available in Project Euclid: 11 February 2010
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Banakh , Taras; Lyaskovska , Nadya; Repovš , Dušan. Packing Index of Subsets in Polish Groups. Notre Dame J. Formal Logic 50 (2009), no. 4, 453--468. doi:10.1215/00294527-2009-021. https://projecteuclid.org/euclid.ndjfl/1265899125