Weekly research seminar
Organizers
 prof. dr hab. Witold Marciszewski
 prof. dr hab. Piotr Zakrzewski
Information
Wednesdays, 4:15 p.m. , room: 5050Research fields
List of talks

Dec. 1, 2021, 4:15 p.m.
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 …

Nov. 24, 2021, 4:15 p.m.
Alberto Salguero Alarcón (Universidad de Extremadura, Badajoz, Spain)
K)space is not a threespace propert (To be a C)
In the setting of Banach spaces, a property P is said to be a threespace property if whenever a Banach space X has a subspace Y so that both Y and the quotient space X/Y …

Nov. 17, 2021, 4:15 p.m.
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 …

Nov. 3, 2021, 4:15 p.m.
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 …

Oct. 27, 2021, 4:15 p.m.
Grzegorz Plebanek (University of Wrocław)
On kappaCorson compacta
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; kappaCorson compactness is defined in the …

Oct. 20, 2021, 4:15 p.m.
Jacek Tryba (University of Gdańsk)
Different kinds of density ideals
We consider several kinds of ideals described by some densities. We present connections between ErdosUlam, density, matrix summability and generalized density ideals and show that a certain inaccuracy in Farah's definition of density ideals leads …

Oct. 13, 2021, 4:15 p.m.
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 nonmeager set with the Baire …

June 9, 2021, 4:15 p.m.
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 …

June 2, 2021, 4:15 p.m.
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 …

May 26, 2021, 4:15 p.m.
Taras Banakh (Ivan Franko National University of Lviv and UJK Kielce)
A universal coregular countable secondcountable 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 …

May 19, 2021, 4:15 p.m.
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 BorodulinNadzieja, is our theorem presented by him recently at this seminar, characterizing a special class of compact spaces without convergent sequences in …

May 12, 2021, 4:15 p.m.
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 …

May 5, 2021, 4:15 p.m.
Jakub Andruszkiewicz (University of Warsaw)
Shelah's proof of diamond
It is a wellknown fact that the diamond principle implies CH, but the reverse implication does not hold. The situation for successor cardinals larger than the first uncountable cardinal is quite different  as proved …

April 28, 2021, 4:15 p.m.
Piotr Zakrzewski (University of Warsaw)
On countably perfectly meager sets
We study a strengthening of the notion of a perfectly meager set. We say that that a subset A of a perfect Polish space X is countably perfectly meager in X if for every sequence …

April 21, 2021, 4:15 p.m.
Piotr BorodulinNadzieja (University of Wrocław)
On forcing names for ultrafilters
We show a way to handle names for ultrafilters in the random forcing. Using this approach we reprove Kunen's theorem about long towers in the random model and Kamburelis' characterization of Boolean algebras supporting finitely …