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Cotygodniowe seminarium badawcze
2020-12-09, godz. 16:15, Zoom
Antonio Aviles Lopez (Universidad de Murcia)
The category of Banach lattices
We shall review some recent developments in the study of the category of Banach lattices: Free, projective, injective objects, etc. Analogies and differences with Banach spaces will be highlighted. This is part of joint works with G. Martinez Cervantes, J. Rodriguez, J. D. Rodriguez Abellan, P. Trad...
2020-12-02, godz. 16:15, Zoom
Piotr Szewczak (Cardinal Stefan Wyszyński University in Warsaw)
Abstract colorings, games and ultrafilters
During the talk we consider various kinds of Ramsey-type theorems. Bergelson and Hindman investigated finite colorings of the complete graph [N]^2 with vertices in natural numbers, involving an algebraic structure of N. It follows from their result that for each finite coloring of [N]^2, there are f...
2020-11-25, godz. 16:15, Zoom
Jan van Mill (University of Amsterdam)
We sketch the proof of the following result: the existence of a normal space whose modal logic coincides with the modal logic of the Kripke frame isomorphic to the power set of a two element set is equivalent to the existence of a measurable cardinal. Whether normal in this result can be weakened to...
2020-11-18, godz. 16:15, Zoom
Lyubomyr Zdomskyy (Institut für Mathematik, Kurt Gödel Research Center, Universität Wien)
Between the Pytkeev and Frechet-Urysohn properties of function spaces
In this talk we aim to compare the Frechet-Urysohn property and some of its formal weakenings for spaces of the form C_p(X). In particular, we plan to present a sketch of the construction under CH of a set of reals X such that C_p(X) has the Pytkeev property (i.e., for every subset A of C_p(X) co...
2020-11-04, godz. 16:15, Zoom
Maciej Malicki (IMPAN)
Non-locally compact Polish groups and non-essentially countable orbit equivalence relations
It is a long-standing open question whether every Polish group that is not locally compact admits a Borel action on a standard Borel space whose associated orbit equivalence relation is not essentially countable. In the talk, I will answer this question positively for the class of all Polish groups ...
2020-10-28, godz. 16:15, Zoom
Taras Banakh (Ivan Franko National University of Lviv and UJK Kielce)
Small uncountable cardinals in asymptology
In the talk we shall discuss some cardinal characteristics of the continuum that appear in large-scale topology, usually as the smallest weights of coarse structures that belong to certain classes (indiscrete, inseparable, large) of finitary or locally finite coarse structures on $\omega$. Besides w...
2020-03-11, godz. 16:15, 5050
Ziemowit Kostana (University of Warsaw)
Cohen-like poset for adding automorphisms of Fraisse limits
There exists a natural forcing notion which turns the set of integers into a Fraisse limit of a given Fraisse class. This long-known phenomenon provided a rough intuition that Fraisse limits, as "generic structures", have some connections with forcing. I investigate a version of this forcing, which ...
2020-03-04, godz. 16:15, 5050
Witold Marciszewski (University of Warsaw)
Complemented subspaces of function spaces C_p(X\times Y), sequences of measures, and ultrafilters
The result of Schachermayer and Cembranos asserts that, for a compact space K, the Banach space C(K) of continuous real valued maps on K, contains a complemented copy of the Banach space c_0 if and only if K admits a sequence of regular Borel measures which is weak* convergent, but not weakly conv...
2020-02-26, godz. 16:15, 5050
Piotr Borodulin-Nadzieja (University of Wrocław)
Analytic P-ideals and Banach spaces
I will talk about certain symmetries between analytic P-ideals and Banach spaces with unconditional bases (e.g. I will give some examples of Banach spaces motivated by ideals and vice-versa). I will present a theorem saying that ideals induced by compact families of finite sets are not F_sigma (and ...
2020-01-22, godz. 16:15, 5050
Adam Kwela (University of Gdańsk)
We will be interested in the following notions of smallness: a subset A of an abelian Polish group X is called Haar-countable/Haar-finite/Haar-n if there are a Borel set B containing A and a copy C of the Cantor set in X such that (C+x)\cap B is countable/finite/of cardinality at most n, for all...
