Abstract
We say that an ideal \({\mathcal{I}}\) on \({\omega}\) is homogeneous, if its restriction to any \({\mathcal{I}}\)-positive subset of \({\omega}\) is isomorphic to \({\mathcal{I}}\). The paper investigates basic properties of this notion — we give examples of homogeneous ideals and present some applications to topology and ideal convergence. Moreover, we answer questions related to our research posed in [1].
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The first author was supported by the grant BW-538-5100-B298-16.
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Kwela, A., Tryba, J. Homogeneous ideals on countable sets. Acta Math. Hungar. 151, 139–161 (2017). https://doi.org/10.1007/s10474-016-0669-z
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DOI: https://doi.org/10.1007/s10474-016-0669-z
Key words and phrases
- ideal
- filter
- ideal convergence
- homogeneous ideal
- anti-homogeneous ideal
- invariant injection
- bi-invariant injection