Solvability of Rado systems in D-sets

Mathias Beiglböck, V. Bergelson, T. Downarowicz, A. Fish

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

Rado’s Theorem characterizes the systems of homogeneous linear equations having the
property that for any finite partition of the positive integers one cell contains a solution
to these equations. Furstenberg and Weiss proved that solutions to those systems can in
fact be found in every central set. (Since one cell of any finite partition is central, this
generalizes Rado’s Theorem.) We show that the same holds true for the larger class of
D-sets. Moreover we will see that the conclusion of Furstenberg’s Central Sets Theorem is
true for all sets in this class.
OriginalspracheEnglisch
Seiten (von - bis)2565-2571
FachzeitschriftTopology and Its Applications: a journal devoted to general, geometric, set-theoretic and algebraic topology
DOIs
PublikationsstatusVeröffentlicht - 2009

ÖFOS 2012

  • 1010 Mathematik

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