Some kinds of sparseness on the real line and ideals on ω
Abstract
We show that a large class of summable ideals can be defined using a certain kind of “sparseness” of subsets of the line near zero, but it is still an open question whether this gives a characterization of the whole class.
Keywords
summable ideals; O’Malley points
References
2. G. Horbaczewska and W. Wilczynski Topologies similar to the density topology, Atti Sem. Mat. Fis. Univ. Modena 51 (2003), no. 2, 433–439.
3. W. Poreda and W. Wilczyński, Topology similar to the density topology, Bull. Soc. Sci. Lett. Łódź Sér. Rech. Déform. 34 (2001), 55–60.
4. W. Wilczyński, Density topologies, in: E. Pap (ed.), Handbook of Measure Theory, North Holland, Amsterdam, 2002, pp. 675–702.
5. W. Wilczyński, Ł. Wojdowski and W. Wojdowski, Points of density and ideals of subsets of N, Georgian Math. J. 26 (2019), no. 4, 529–535.
Wydział Matematyki i Informatyki, Uniwersytet Łódzki Poland
Wydział Matematyki i Informatyki, Uniwersytet Łódzki Poland
https://orcid.org/0000-0002-2883-0941
The Copyright Holders of the submitted text are the Author and the Journal. The Reader is granted the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution (CC BY). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.
- License
This journal provides immediate open access to its content under the Creative Commons BY 4.0 license (http://creativecommons.org/licenses/by/4.0/). Authors who publish with this journal retain all copyrights and agree to the terms of the above-mentioned CC BY 4.0 license. - Author’s Warranties
The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s. - User Rights
Under the Creative Commons Attribution license, the users are free to share (copy, distribute and transmit the contribution) and adapt (remix, transform, and build upon the material) the article for any purpose, provided they attribute the contribution in the manner specified by the author or licensor. - Co-Authorship
If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.