Families of Increasing Sequences Possessing the Harmonic Series Property

• Autorzy: Wituła, Roman , Hetmaniok, Edyta , Słota, Damian

Abstrakty

EN

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.

Słowa kluczowe

EN

Sierpiński family; harmonic series property

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Acta Universitatis Lodziensis. Folia Mathematica
• Rocznik: 2013
• Tom: vol. 18

Daty

wydano

2013

Twórcy

autor

Wituła, Roman

autor

Hetmaniok, Edyta

autor

Słota, Damian

other

Institute of Mathematics, Silesian University of Technology

other

[e-mail]

Identyfikatory

URI

http://hdl.handle.net/11089/6449