Abstract
The aim of this paper is to demonstrate the existence of a proper ideal on the Cantor space that contains three well-known ideals. Our construction is based on specific operations that can be considered as tools for generating new sets. Additionally, we examine several properties of the sets produced in this way.
References
[1] P. Eliaš, Dirichlet sets, Erdős–Kunen–Mauldin theorem, and analytic subgroups of the reals, Proc. Amer. Math. Soc. 139 (2011), no. 6, 2093–2104. 10.1090/S0002-9939-2010-10639-1Search in Google Scholar
[2] R. Filipów, On Hindman spaces and the Bolzano–Weierstrass property, Topology Appl. 160 (2013), no. 15, 2003–2011. 10.1016/j.topol.2013.08.007Search in Google Scholar
[3] J. Flašková, Ultrafilters and small sets, PhD thesis, Univerzita Karlova, 2006. Search in Google Scholar
[4] N. Hindman, Finite sums from sequences within cells of a partition of N, J. Combin. Theory Ser. A 17 (1974), 1–11. 10.1016/0097-3165(74)90023-5Search in Google Scholar
[5] M. Hrušák and D. Meza-Alcántara, Universal submeasures and ideals, Questions Answers Gen. Topology 31 (2013), no. 2, 65–69. Search in Google Scholar
[6] P. Klinga, A. Nowik and A. Wąsik, σ-porosity of certain ideals, preprint (2025), https://arxiv.org/abs/2512.07711. Search in Google Scholar
[7] K. Kowitz, The use of Katětov order in the study of topological spaces and ultrafilters, PhD thesis, University of Gdańsk, 2023. Search in Google Scholar
[8]
K. Mazur,
[9] A. Nowik and P. Szyszkowska, On some relations between ideals of nowhere dense sets in topologies on positive integers, Period. Math. Hungar. 85 (2022), no. 1, 164–170. 10.1007/s10998-021-00426-6Search in Google Scholar
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