Name
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 vertical bar S vertical bar of subsets S c G such that the family of shifts {xA}(x is an element of S) is (almost) disjoint (in the sense that vertical bar xA boolean AND yA vertical bar < vertical bar G vertical bar for any distinct points x, y is an element of S). Subsets A c G with small (almost) packing index are large in a geometric sense. We show that pack(A) is an element of N boolean OR {N(0), c} for any sigma-compact subset A of a Polish group. In each nondiscrete Polish Abelian group G we construct two closed subsets A, B subset of G with pack(A) = pack(B) = c and Pack(A boolean OR B) = 1 and then apply this result to show that G contains a nowhere dense.Haar null subset C subset of G with pack(C) = Pack(C) = kappa for any given cardinal number kappa is an element of [4, c]. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1215/00294527-2009-021 | NOTRE DAME JOURNAL OF FORMAL LOGIC |
Keywords | Field | DocType |
Polish group,packing index,Borel set,Haar null set,Martin axiom,continuum hypothesis | Discrete mathematics,Abelian group,Combinatorics,Uncountable set,Nowhere dense set,Disjoint sets,Infimum and supremum,Cardinality,Mathematics,Continuum hypothesis,Borel set | Journal |
Volume | Issue | ISSN |
50 | 4 | 0029-4527 |
Citations | PageRank | References |
1 | 0.48 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Taras O. Banakh | 1 | 9 | 7.24 |
| Nadia Lyaskovska | 2 | 2 | 1.23 |
| Dusan Repovš | 3 | 21 | 11.09 |