Weekly research seminar

2022-03-30, 16:15, 4420

Robert Rałowski (University of Wrocław)

The two-dimensional version of Mycielski theorem says that for every comeager or conull subset G of the real plane there exists a perfect subset of the real line such that the square of this perfect set P can be inscribed into set G modulo diagonal. We consider a strengthening of this theorem by r...

2022-03-23, 16:15, 4420

Piotr Szewczak (Cardinal Stefan Wyszyński University in Warsaw)

**Strongly sequentially separable function spaces**A space is Frechet–Urysohn if each point in the closure of a set is a limit of a sequence from the set. A separable space is strongly sequentially separable if, for each countable dense set, every point in the space is a limit of a sequence from the dense set. Applying methods of selection ...

2022-03-16, 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, 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, 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, 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, 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, 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, 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, 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(...