October 2022
Adam Morawski: P-measures in models without P-points
20/10/22 14:47
Tuesday, October 25, 2022 17:00
Location: room C11-3.11
Speaker: Adam Morawski
Title: P-measures in models without P-points
Abstract: P-points are ultrafilters in which every decreasing sequence of sets from the filter has a pseudointersection (in a sense an intersection modulo finite sets) in the filter. Quite similarly P-measures (known in the literature as measures with additive property*) are finitely additive probability measures in which every decreasing sequence of sets has a pseudointersection with measure equal to the limit of measures of sets from the sequence.
It is not hard to see that (a characteristic function of) a P-point is a P-measure. However, a question whether the existence of P-measures implies the existence of P-points remains open.
I will talk about current knowledge of the problem including my and Piotr Borodulin-Nadzieja's efforts and results - based on the Silver forcing and its variations.
Location: room C11-3.11
Speaker: Adam Morawski
Title: P-measures in models without P-points
Abstract: P-points are ultrafilters in which every decreasing sequence of sets from the filter has a pseudointersection (in a sense an intersection modulo finite sets) in the filter. Quite similarly P-measures (known in the literature as measures with additive property*) are finitely additive probability measures in which every decreasing sequence of sets has a pseudointersection with measure equal to the limit of measures of sets from the sequence.
It is not hard to see that (a characteristic function of) a P-point is a P-measure. However, a question whether the existence of P-measures implies the existence of P-points remains open.
I will talk about current knowledge of the problem including my and Piotr Borodulin-Nadzieja's efforts and results - based on the Silver forcing and its variations.
Antonio Martínez Celis Rodríguez: Some combinatorics related to the Michael space problem
17/10/22 19:07
Tuesday, October 18, 2022 17:00
Location: room C11-3.11
Speaker: Antonio Martínez Celis Rodríguez
Title: Some combinatorics related to the Michael space problem
Abstract: A Lindelöf space is Michael if it has non-Lindelöf product with the Baire space. In this talk (series of talks?) we will review some of the combinatorics required to construct one of these spaces. The main goal is to show that the existence of a selective ultrafilter (plus \(\varepsilon\ge 0\)) is enough to construct a Michael space.
Location: room C11-3.11
Speaker: Antonio Martínez Celis Rodríguez
Title: Some combinatorics related to the Michael space problem
Abstract: A Lindelöf space is Michael if it has non-Lindelöf product with the Baire space. In this talk (series of talks?) we will review some of the combinatorics required to construct one of these spaces. The main goal is to show that the existence of a selective ultrafilter (plus \(\varepsilon\ge 0\)) is enough to construct a Michael space.
Paweł Krupski: On the hyperspace of simple closed curves in the plane
13/10/22 14:46
Tuesday, October 11, 2022 17:00
Location: room C11-3.11
Speaker: Paweł Krupski
Title: On the hyperspace of simple closed curves in the plane
Abstract: The Vietoris hyperspace of simple closed curves in the plane will be discussed toward its desirable characterization. In particular, the local contractibility will be shown.
Joint work with Krzysztof Omiljanowski.
Location: room C11-3.11
Speaker: Paweł Krupski
Title: On the hyperspace of simple closed curves in the plane
Abstract: The Vietoris hyperspace of simple closed curves in the plane will be discussed toward its desirable characterization. In particular, the local contractibility will be shown.
Joint work with Krzysztof Omiljanowski.