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Cotygodniowe seminarium badawcze
2022-12-21, godz. 16:15, 5050
Damian Sobota (Universität Wien, Kurt Gödel Research Center for Mathematical Logic)
On continuous operators from Banach spaces of Lipschitz functions onto c_0
During my talk I will discuss some of our recent results concerning the existence of continuous operators from the Banach spaces Lip_0(M) of Lipschitz real-valued functions on metric spaces M onto the Banach space c_0 of sequences converging to 0. I will in particular prove that there is always a co...
2022-12-14, godz. 16:15, 5050
Piotr Koszmider (IM PAN)
The density of a topological vector space (tvs) X is the minimal cardinality of a dense subset of X. A subset of a tvs is called linearly dense if the set of all linear combinations of its elements forms a dense subset. A subset Y of a tvs X is called overcomplete if it has cardinality equ...
2022-12-07, godz. 16:15, 5050
Tomasz Kania (Jagiellonian University)
A biorthogonal system in a Banach space is called Auerbach whenever both the vectors and the associated functionals are precisely of norm 1. We will show that assuming the Continuum Hypothesis, there exist renormings of c_0(\omega_1) that do not contain uncountable Auerbach systems, which contrasts ...
2022-11-30, godz. 16:15, 5050
Witold Marciszewski (University of Warsaw)
On \omega-Corson compact spaces and related classes of Eberlein compacta
Recall that a compact space K is Eberlein compact if it can be embedded into some Banach space X equipped with the weak topology. A compact space K is \omega-Corson compact if, for some set \Gamma, K is homeomorphic to a subset of the \sigma-product of real lines \sigma(R^\Gamma), i.e. the subspace ...
2022-11-16, godz. 16:15, Zoom
Lyubomyr Zdomskyy (Technische Universität Wien)
On cardinalities of Lindelöf first countable spaces
We shall present the main ideas of the construction of a Lindelöf first countable T_1 space of cardinality bigger than continuum. This is a modification of an earlier construction invented by Gorelic. It is well-known that there are no such T_2 spaces. The talk is going to be based on a work i...
2022-11-09, godz. 16:15, 5050
Mikołaj Krupski (University of Warsaw)
\kappa-pseudocompactness and uniform homeomorphisms of function spaces
A Tychonoff space X is called \kappa-pseudocompact if for every continuous mapping f of X into R^\kappa the image f(X) is compact. This notion generalizes pseudocompactness and gives a stratification of spaces lying between pseudocompact and compact spaces. It is well known that pseudocompactness ...
2022-10-26, godz. 16:15, 5050
Maciej Malicki (IM PAN)
Isomorphism of locally compact Polish metric structures
Gao and Kechris asked if the isometry relation on the space of locally compact Polish metric spaces is (Borel) reducible to the isomorphism relation of countable graphs. It turns out that this question is easier to deal with if it is translated to the language of metric structures and continuous log...
2022-10-19, godz. 16:15, 5050
Paweł Krupski (Wrocław University of Science and Technology)
On the hyperspace of simple closed curves in the plane
The Vietoris hyperspace of simple closed curves in the plane will be discussed. Its characterization is a challenging open problem. An elementary proof of the hyperspace's local contractibility will be presented. Joint work with Krzysztof O...
2022-06-08, godz. 16:15, 4420
Wiesław Kubiś (Institute of Mathematics of the Czech Academy of Sciences and Cardinal Stefan Wyszyński University in Warsaw)
Linear spaces are basic incidence structures consisting of points and lines, These are in fact first order structures naturally encoded by a single ternary relation. We shall discuss homogeneity questions, namely, when every small partial isomorphism extends to an automorphism. We show that the only...
2022-06-01, godz. 16:15, 4420
Mikołaj Krupski (University of Warsaw)
Preservation of some covering type properties by linear homeomorphisms of function spaces: Part 2
In the second part of my talk I will show some proof techniques. The talk should be accessible regardless of listening to part 1. An old question of Arhangel'skii asks if (a) the Lindelof property (b) the Menger property of a Tychonoff space X is preserved by homeomorphisms of the spac...
