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2009 Packing Index of Subsets in Polish Groups
Taras Banakh , Nadya Lyaskovska , Dušan Repovš
Notre Dame J. Formal Logic 50(4): 453-468 (2009). DOI: 10.1215/00294527-2009-021

Abstract

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 S G such that the family of shifts x A x S is (almost) disjoint (in the sense that x A y A < G for any distinct points x , y S ). Subsets A G with small (almost) packing index are large in a geometric sense. We show that pack A 0 c for any σ-compact subset A of a Polish group. In each nondiscrete Polish Abelian group G we construct two closed subsets A , B G with pack A = pack B = c and Pack ( A B ) = 1 and then apply this result to show that G contains a nowhere dense Haar null subset C G with pack(C)=Pack(C)=κ for any given cardinal number κ 4 c .

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Taras Banakh . Nadya Lyaskovska . Dušan Repovš . "Packing Index of Subsets in Polish Groups." Notre Dame J. Formal Logic 50 (4) 453 - 468, 2009. https://doi.org/10.1215/00294527-2009-021

Information

Published: 2009
First available in Project Euclid: 11 February 2010

zbMATH: 1203.03066
MathSciNet: MR2598874
Digital Object Identifier: 10.1215/00294527-2009-021

Subjects:
Primary: 03E15 , 03E17 , 03E35 , 03E50 , 03E75 , 05D99
Secondary: 22A99 , 54H05 , 54H11

Keywords: Borel set , Continuum hypothesis , Haar null set , Martin axiom , packing index , Polish group

Rights: Copyright © 2009 University of Notre Dame

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Vol.50 • No. 4 • 2009
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