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Cotygodniowe seminarium badawcze
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...
2021-06-09, godz. 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, godz. 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, godz. 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, godz. 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, godz. 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...
2021-05-05, godz. 16:15, Zoom
Jakub Andruszkiewicz (University of Warsaw)
It is a well-known 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 by Shelah, if only cardinal kappa is uncountable, then 2^kappa = kappa^+ is enough...
2021-04-28, godz. 16:15, Zoom
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 (P_n) of perfect subsets of X, there is an F_sigma set F in X containing A and such that the intersection of F with P_n i...
