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Generating new ideals using weighted density via modulus functions
- Source :
- Indagationes Mathematicae. 29:1196-1209
- Publication Year :
- 2018
- Publisher :
- Elsevier BV, 2018.
-
Abstract
- In this paper we extend the idea of weighted density of Balcerzak et al. (2015) by using a modulus function and introduce the idea f -density of weight g of subsets of ω ≔ { 0 , 1 , … } (at the same time extending the notion of f -density (Aizpuru et al., 2014)), which we name d g f where g : ω → [ 0 , ∞ ) satisfies g ( n ) → ∞ and n ∕ g ( n ) ↛ 0 and f is a modulus function. The aim of this paper is to show that we can get new ideals Z g ( f ) consisting of sets A ⊂ ω for which d g f ( A ) = 0 different from all the previously constructed ideals Z g of Balcerzak et al. (2015) and moreover they retain all the nice properties of the ideals Z g .
Details
- ISSN :
- 00193577
- Volume :
- 29
- Database :
- OpenAIRE
- Journal :
- Indagationes Mathematicae
- Accession number :
- edsair.doi...........ce0d24faec936fcf2722a6f762415898