 Nie jesteś zalogowany | zaloguj się |
| Nie jesteś zalogowany | zaloguj się |
Cotygodniowe seminarium badawcze
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...
2021-04-21, godz. 16:15, Zoom
Piotr Borodulin-Nadzieja (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 additive measures. The talk represents joint works with Dami...
2021-04-14, godz. 16:15, Zoom
Ziemowit Kostana (University of Warsaw)
What would the rational Urysohn space and the random graph look like if they were uncountable?
We apply the technology developed in the 80s by Avraham, Rubin, and Shelah, to prove that the following is consistent with ZFC: there exists an uncountable, separable metric space X with rational distances, such that every uncountable partial 1-1 function from X to X is an isometry on an uncountable...
2021-03-24, godz. 16:15, Zoom
Grzegorz Plebanek (University of Wrocław)
Weakly Radon-Nikodym Boolean algebras
Weakly Radon-Nikodym (WRN) Boolean algebras are named after a certain class of compacta related to Banach spaces but they can be charaterized as those algebras that have, in a sense, few independent sequences. We compare the class of WRN algebras with some others, such as minimally generated algebra...
