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Cotygodniowe seminarium badawcze
2022-01-12, godz. 16:15, 4420
Maciej Malicki (IMPAN)
Large conjugacy classes and weak amalgamation
Ivanov, and later Kechris and Rosendal, characterized the existence of dense or comeager (diagonal) conjugacy classes in automorphism groups of certain classes of Fraïssé limits. I will show how these results can be extended to limits of weak Fraïssé classes, using an approac...
2021-12-15, godz. 16:15, Zoom
Sławomir Solecki (Cornell University)
Closed groups generated by generic measure preserving transformations
The behavior of a measure preserving transformation, even a generic one, is highly nonuniform. In contrast to this observation, a different picture of a very uniform behavior of the closed group generated by a generic measure preserving transformation T has emerged. This picture included substantial...
2021-12-08, godz. 16:15, Zoom
Paul Szeptycki (York University)
On a topological Ramsey theorem
This is joint work with Wiesław Kubiś. We introduce natural strengthenings of sequential compactness called the $r$-Ramsey property for each natural number $r\geq 1$. We prove that metrizable compact spaces are $r$-Ramsey for all $r$ and give examples of compact spaces that are $r$-Ramsey bu...
2021-12-01, godz. 16:15, Zoom
Piotr Szewczak (Cardinal Stefan Wyszyński University in Warsaw)
Products of Hurewicz, Menger and Lindelof spaces - a continuation
We consider products of general topological spaces with Hurewicz’s, Menger’s and Lindelof’s covering properties. Assuming the Continuum Hypothesis, we prove that every productively Lindelof space is productively Menger, and every productively Menger space is productively Hurewicz. ...
2021-11-24, godz. 16:15, Zoom
Alberto Salguero Alarcón (Universidad de Extremadura, Badajoz, Spain)
To be a C(K)-space is not a three-space property
In the setting of Banach spaces, a property P is said to be a three-space property if whenever a Banach space X has a subspace Y so that both Y and the quotient space X/Y satisfy P, then X also satisfies P. It has been known for some time that ``to be isomorphic to a space of continuous functions C(...
2021-11-17, godz. 16:15, Zoom
Jan van Mill (University of Amsterdam)
Universal autohomeomorphisms of $N^*$
This is joint work with Klaas Pieter Hart. We study the existence of universal autohomeomorphisms of $N^*$. We prove that CH implies there is such an autohomeomorphism and show that there are none in any model where all autohomeomorphisms of $N^*$ are trivial. ...
2021-11-03, godz. 16:15, 4420
Piotr Szewczak (Cardinal Stefan Wyszyński University in Warsaw)
Products of Hurewicz, Menger and Lindelof spaces
We consider products of general topological spaces with Hurewicz’s, Menger’s and Lindelof’s covering properties. Assuming the Continuum Hypothesis, we prove that every productively Lindelof space is productively Menger, and every productively Menger space is productively Hurewicz. ...
2021-10-27, godz. 16:15, 4420
Grzegorz Plebanek (University of Wrocław)
A compact space is `Corson compact' if it can be embedded into some product of real lines in such a way that the support of every element is countable; kappa-Corson compactness is defined in the same manner, replacing `countable' by `of size < kappa'. That class of kappa-Corson compac...
2021-10-20, godz. 16:15, Zoom
Jacek Tryba (University of Gdańsk)
Different kinds of density ideals
We consider several kinds of ideals described by some densities. We present connections between Erdos-Ulam, density, matrix summability and generalized density ideals and show that a certain inaccuracy in Farah's definition of density ideals leads to Farah's characterization when density ide...
2021-10-13, godz. 16:15, 4420
Tomasz Weiss (Cardinal Wyszyński University in Warsaw)
On the algebraic sum of a perfect set and a large subset of the reals
In M. Kysiak’s paper "Nonmeasurable algebraic sums of sets of reals", (Coll. Math., Vol. 102, No 1, 2005), the following two questions appeared. Assume that A ⊆ R is a non-meager set with the Baire property and P is perfect. Do there exist meager sets X ⊆ A and Y ⊆ P s...
