Geodesic
Families of Increasing Sequences Possessing the Harmonic Series Property
Acta Universitatis Lodziensis. Folia Mathematica, Tome 18 (2013).

Voir la notice de l'article provenant de la source University of Lodz Repository

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.
Mots-clés : Sierpiński family, harmonic series property 
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Wituła, Roman; Hetmaniok, Edyta; Słota, Damian. Families of Increasing Sequences Possessing the Harmonic Series Property. Acta Universitatis Lodziensis. Folia Mathematica, Tome 18 (2013). http://geodesic.mathdoc.fr/item/AULFM_2013_18_a3/