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## Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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# Seminarium „Topologia i teoria mnogości”

5050

## Lista referatów

• 2022-03-16, godz. 16:15, 4420

Piotr Koszmider (IM PAN)

Almost disjoint families and the geometry of spheres

We present an example of a nonseparable Banach space where every uncountable subset of the unit sphere contains two vectors which are distant by less than one. This solves in the negative the central problem of the search for a nonseparable version of Kottman’s theorem which has produced man...

• 2022-01-26, godz. 16:15, Zoom

Taras Banakh (Ivan Franko National University of Lviv and UJK Kielce)

Automatic continuity of measurable homomorphisms on topological groups

We shall discuss three recent results on automatic continuity of homomorphisms: 1) Every Haar-measurable homomorphism from a locally compact group to an arbitrary topological group is continuous. 2) Every homomorphism with the Baire property from an $\omega$-narrow Cech-complete topologic...

• 2022-01-19, godz. 16:15, Zoom

Wiesław Kubiś (Cardinal Stefan Wyszyński University in Warsaw and Institute of Mathematics of the Czech Academy of Sciences)

Abstract evolution systems, amalgamation and homogeneity

An evolution system is just a category with a distinguished class of arrows, called transitions. This concept, in particular, generalizes abstract rewriting system. It turns out that evolution systems with amalgamation provide a good framework for studying homogeneous structures, both finite and i...

• 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

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. ...