Jarosław Swaczyna: Generalized densities of subsets of natural numbers and associated ideals
15/05/15 19:36
Tuesday, May 19, 2015 17:15
Room: D1-215
Speaker: Jarosław Swaczyna
Title: Generalized densities of subsets of natural numbers and associated ideals
Abstract. Let \(g: \omega \rightarrow [0, \infty)\). We say that \(A \subset \omega\) has \(g\)-density zero, if \(\lim_{n \rightarrow \infty} \frac{A \cap n}{g(n)} = 0\). It is an easy observation that family of \(g\)-density zero sets is an ideal.
I will discuss some properties of ideals obtained this way (among others, I will show that they can be generated using Solecki's submeasures). I will then examine inclusions between ideals obtained for different functions \(g\).
I will also discuss connections between our ideals, "density-like" ideals and Erdos-Ulam ideals. I will present joint results with M. Balcerzak, P. Das and M. Filipczak.
Room: D1-215
Speaker: Jarosław Swaczyna
Title: Generalized densities of subsets of natural numbers and associated ideals
Abstract. Let \(g: \omega \rightarrow [0, \infty)\). We say that \(A \subset \omega\) has \(g\)-density zero, if \(\lim_{n \rightarrow \infty} \frac{A \cap n}{g(n)} = 0\). It is an easy observation that family of \(g\)-density zero sets is an ideal.
I will discuss some properties of ideals obtained this way (among others, I will show that they can be generated using Solecki's submeasures). I will then examine inclusions between ideals obtained for different functions \(g\).
I will also discuss connections between our ideals, "density-like" ideals and Erdos-Ulam ideals. I will present joint results with M. Balcerzak, P. Das and M. Filipczak.