Maciej Korpalski
Maciej Korpalski: Straightening almost chains into barely altenating ones
23/10/23 10:34
Tuesday, October 24, 2023 17:00
Location: room 601, Mathematical Institute, University of Wroclaw
Speaker: Maciej Korpalski
Title: Straightening almost chains into barely altenating ones
Abstract: Consider an almost chain \(\mathcal{A} = \{A_x \subset \omega: x \in X\}\) for some separable linearly ordered set \(X\). Such a chain is barely alternating if for all \(n \in \omega\) we cannot find elements \(x_1 < x_2 < x_3 < x_4\) in \(X\) satisfying \(n \in A_{x_1}, A_{x_3}\), \(n \notin A_{x_2}, A_{x_4}\). We will show that under \(MA(\kappa)\), if \(|X| \leq \kappa\), then we can straighten our almost chain \(\mathcal{A}\) into a barely alternating one by changing at most finitely many elements in each set \(A_x\).
Location: room 601, Mathematical Institute, University of Wroclaw
Speaker: Maciej Korpalski
Title: Straightening almost chains into barely altenating ones
Abstract: Consider an almost chain \(\mathcal{A} = \{A_x \subset \omega: x \in X\}\) for some separable linearly ordered set \(X\). Such a chain is barely alternating if for all \(n \in \omega\) we cannot find elements \(x_1 < x_2 < x_3 < x_4\) in \(X\) satisfying \(n \in A_{x_1}, A_{x_3}\), \(n \notin A_{x_2}, A_{x_4}\). We will show that under \(MA(\kappa)\), if \(|X| \leq \kappa\), then we can straighten our almost chain \(\mathcal{A}\) into a barely alternating one by changing at most finitely many elements in each set \(A_x\).
Maciej Korpalski: Continuous discrete extension of double arrow spaces
27/03/22 21:03
Tuesday, March 29, 2022 17:00
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Maciej Korpalski
Title: Continuous discrete extension of double arrow spaces
Abstract: Double arrow space is a separable linearly ordered compact space. By adding a discrete countable set in a special way we can extend those spaces so that extension is still compact. We will talk about some properties of those extensions and see counterexamples to them.
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Maciej Korpalski
Title: Continuous discrete extension of double arrow spaces
Abstract: Double arrow space is a separable linearly ordered compact space. By adding a discrete countable set in a special way we can extend those spaces so that extension is still compact. We will talk about some properties of those extensions and see counterexamples to them.
Maciej Korpalski: Combinatorial characterization of null set covering
14/11/21 09:06
Tuesday, November 16, 2021 17:00
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Maciej Korpalski
Title: Combinatorial characterization of null set covering
Abstract: In this talk we will recall a result from Bartoszynski regarding partial characterization of covering coefficient of ideal formed by sets with Lebesgue measure equal to zero. This is done in terms of slaloms and small sets. This theorem's proof had some problems along the way and we will see how to fix them.
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Maciej Korpalski
Title: Combinatorial characterization of null set covering
Abstract: In this talk we will recall a result from Bartoszynski regarding partial characterization of covering coefficient of ideal formed by sets with Lebesgue measure equal to zero. This is done in terms of slaloms and small sets. This theorem's proof had some problems along the way and we will see how to fix them.