Weekly research seminar

2022-11-09, 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, 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, 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, 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, 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...

2022-05-25, 16:15, 4420

Mikołaj Krupski (University of Warsaw)

**Preservation of some covering type properties by linear homeomorphisms of function spaces**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 space C_p(X) of continuous functions on X equipped with the pointwise topology. A celebrated Velichko's theorem [Topol. Appl. 89, (1998)] pr...

2022-05-18, 16:15, 4420

Damian Głodkowski (University of Warsaw)

**A Banach space C(K) reading the dimension of K**We show that if Jensen's diamond principle holds, then for every natural number n there is a compact space K, such that whenever L is compact space and the Banach spaces of continuous functions C(K) and C(L) are isomorphic, the covering dimension of L is equal to n. The constructed space K is a ...

2022-05-11, 16:15, 4420

Tomasz Cieśla (Lancaster University)

**On random compact sets, equidecomposition and domains of expanison in R^3**We describe a certain model of random compact sets. We use it to construct a pair of compact sets A and B in R^3 of the same Lebesgue measure such that A can be covered by finitely many translates of B and vice versa, yet A and B are not equidecomposable. We also give the first example of a compact ...

2022-04-27, 16:15, 4420

Ziemowit Kostana (Bar-Ilan University)

Parametrized diamonds are combinatorial principles that imply many consequences of the original Jensen's Diamond, yet are consistent with the CH failing. Informally speaking, they are in similar relation to Jensen's Diamond, as cardinal invariants of the Cichoń's diagram are to CH. The modern frame...

2022-04-06, 16:15, Zoom

Antonio Aviles Lopez (Universidad de Murcia)

**Topological properties in tensor products of Banach spaces**We will expose a recent work with G. Martinez Cervantes, J. Rodriguez and A. Rueda Zoca where we study several topological properties (like weakly compactly generated, weakly Lindelöf determined, property (C) of Corson...) on tensor products of Banach spaces. ...