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Topology and Set Theory Seminar

Weekly research seminar

Organizers

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Wednesdays, 4:15 p.m. , room: 5050

Research fields

List of talks
  • 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 kappa-Corson 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; kappa-Corson 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 Erdos-Ulam, 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 non-meager 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 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 …
  • 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 Borodulin-Nadzieja, 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 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 …
  • 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 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 …
  • April 14, 2021, 4:15 p.m.
    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 …
  • March 24, 2021, 4:15 p.m.
    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 …
  • March 17, 2021, 4:15 p.m.
    Damian Głodkowski (University of Warsaw)
    Coverings of Banach spaces and their subsets by hyperplanes
    A hyperplane of a Banach space is a closed one-codimensional subspace. Hyperplanes are nowhere dense and so, no countable collection of hyperplanes can cover the entire space. Given a Banach space we consider the \sigma-ideal …

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