Some new facts about group 𝒢 generated by the family of convergent permutations

• Autorzy: Roman Wituła , Edyta Hetmaniok , Damian Słota
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to present some new and essential facts about group 𝒢 generated by the family of convergent permutations, i.e. the permutations on ℕ preserving the convergence of series of real terms. We prove that there exist permutations preserving the sum of series which do not belong to 𝒢. Additionally, we show that there exists a family G (possessing the cardinality equal to continuum) of groups of permutations on ℕ such that each one of these groups is different than 𝒢 and is composed only from the permutations preserving the sum of series. This result substantially strengthens some old Pleasants’ result.

Słowa kluczowe

EN

Convergent permutations; Divergent permutations; b-connected permutations

Kategorie tematyczne

• 05A99: None of the above, but in this section
• 40A05: Convergence and divergence of series and sequences

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 568-577

Daty

wydano

2017-05-06

otrzymano

2014-10-27

zaakceptowano

2015-11-09

online

2017-05-06

Twórcy

autor

Roman Wituła

• , , , 44-100,

autor

Edyta Hetmaniok

• , , , 44-100,

autor

Damian Słota

• , , , 44-100,

Identyfikatory

DOI

10.1515/math-2017-0048