Opis

• Title:
  Families of Increasing Sequences Possessing the Harmonic Series Property
• Creator:
  Wituła, Roman;
  Hetmaniok, Edyta;
  Słota, Damian
• Contributor:
  Institute of Mathematics, Silesian University of Technology;
  roman.witula@polsl.pl
• Description:
  We prove in this paper that any maximal, with respect to inclusion, subset of N – the family of all increasing sequences of positive integers – possessing the harmonic series property has the cardinality of the continuum. Moreover, we prove that for any countable (infinite) set exists an "orthogonal" family such that it hold some facts. All facts are proved constructively, by using the modified version of the classical Sierpiński family of increasing sequences having the cardinality of the continuum.
• Object availability:
  Dostęp otwarty
• Rights:
  Uznanie autorstwa-Bez utworów zależnych 3.0 Polska;
  http://creativecommons.org/licenses/by-nd/3.0/pl
• Date:
  2015.01.30;
  2013
• Type:
  Article
• Language:
  angielski
• Format:
  application/pdf
• Publisher:
  Łódź University Press
• Relation:
  Acta Universitatis Lodziensis. Folia Mathematica;1;
  18
• Subject:
  Sierpiński family;
  harmonic series property
• Identifier:
  0208-6204;
  http://hdl.handle.net/11089/6449
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  sprawdź warunki licencji
• Type:
  obrazy