Jacek Tryba: Homogeneity of ideals

Tuesday, March 6, 2018, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Jacek Tryba (University of Gdansk)

Title: Homogeneity of ideals


The homogeneity family of the ideal $\mathcal{I}$ is a family of subsets such that the restriction of $\mathcal{I}$ to this subset is isomorphic to $\mathcal{I}$.
We say that an ideal $\mathcal{I}$ is homogeneous if all $\mathcal{I}$-positive sets belong to the homogeneity family of $\mathcal{I}$. We investigate basic properties of this notion, give examples of homogeneous ideals and present some applications to ideal
Moreover, we present connections between the homogeneity families and the notion of bi-$\mathcal{I}$-invariant functions introduced by Balcerzak, Głąb and Swaczyna and give answers to several questions related to this topic.

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