Approach to the Summable Ideal by O’Malley Density of Special Testing Sets on the Real Line

Małgorzata Filipczak; Grażyna Horbaczewska

doi:10.2478/tmmp-2025-0008

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Approach to the Summable Ideal by O’Malley Density of Special Testing Sets on the Real Line

Tatra Mountains Mathematical Publications

Volume 89 (2025): Issue 1 (September 2025)

By: Małgorzata Filipczak and Grażyna Horbaczewska

Open Access

|Nov 2025

Abstract

The summable ideal for a harmonic series is described by the O’Malley density of subsets of the real line generated by sequences of reals. Since this approach leads to a special kind of summable ideals, we investigate the relationship between them and we find conditions under which summable ideals for specific series coincide with one for the harmonic series.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2025-0008 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 47 - 58

Submitted on: Nov 15, 2024

Accepted on: May 7, 2025

Published on: Nov 29, 2025

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

density,

Related subjects:

© 2025 Małgorzata Filipczak, Grażyna Horbaczewska, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 89 (2025): Issue 1 (September 2025)