Weekly research seminar

2021-11-17, 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, 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, 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, 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, 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...

2021-06-09, 16:15, Zoom

Krzysztof Zakrzewski (University of Warsaw)

**Rosenthal compacta and lexicographic products**For a metrizable space X, by B_1(X) we denote the space of real valued functions of the first Baire class on X, endowed with pointwise convergence topology. A compact space K is called Rosenthal compact if it can be embedded in B_1(X) for some completely metrizable separable space X. We consider two...

2021-06-02, 16:15, Zoom

Andrzej Nagórko (University of Warsaw)

**Property A and duality in linear programming**Property A was introduced in 2000 and turns out to be of great importance in many areas of mathematics. Perhaps the most striking example is the following implication. "If group G has Property A then the Novikov conjecture is true for all closed manifolds with fundamental group G." ...

2021-05-26, 16:15, Zoom

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

**A universal coregular countable second-countable space**A Hausdorﬀ topological space X is called superconnected (resp. coregular) if for any nonempty open sets U_1 , . . . ,U_n ⊆ X, the intersection of their closures cl(U_1)∩...∩cl(U_n) is not empty (resp. the complement X \ (cl(U_1)∩...∩cl(U_n)) is a regular topological space). A canonical ...

2021-05-19, 16:15, Zoom

Damian Sobota (Kurt Gödel Research Center, University of Vienna)

**On sequences of homomorphisms into measure algebras and the Efimov problem**The starting point for my talk, based on the joint work with Piotr Borodulin-Nadzieja, is our theorem presented by him recently at this seminar, characterizing a special class of compact spaces without convergent sequences in the random model. Namely, we proved that if A is a Boolean algebra i...

2021-05-12, 16:15, Zoom

Piotr Koszmider (Institute of Mathematics of the Polish Academy of Sciences)

**Pure states, quantum filters and ultrafilters**We will describe how the usual notion of an ultrafilter on N extends to the notion of a maximal quantum filter. Such objects correspond to pure states of quantum systems the same way that ultrafilters correspond to points of the Cech-Stone compactification of the integers linking set-theory wi...