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Cotygodniowe seminarium badawcze
2022-05-25, godz. 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, godz. 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, godz. 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, godz. 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, godz. 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. ...
2022-03-30, godz. 16:15, 4420
Robert Rałowski (University of Wrocław)
The two-dimensional version of Mycielski theorem says that for every comeager or conull subset G of the real plane there exists a perfect subset of the real line such that the square of this perfect set P can be inscribed into set G modulo diagonal. We consider a strengthening of this theorem by r...
2022-03-23, godz. 16:15, 4420
Piotr Szewczak (Cardinal Stefan Wyszyński University in Warsaw)
Strongly sequentially separable function spaces
A space is Frechet–Urysohn if each point in the closure of a set is a limit of a sequence from the set. A separable space is strongly sequentially separable if, for each countable dense set, every point in the space is a limit of a sequence from the dense set. Applying methods of selection ...
2022-03-16, godz. 16:15, 4420
Piotr Koszmider (IM PAN)
Almost disjoint families and the geometry of spheres
We present an example of a nonseparable Banach space where every uncountable subset of the unit sphere contains two vectors which are distant by less than one. This solves in the negative the central problem of the search for a nonseparable version of Kottman’s theorem which has produced man...
2022-01-26, godz. 16:15, Zoom
Taras Banakh (Ivan Franko National University of Lviv and UJK Kielce)
Automatic continuity of measurable homomorphisms on topological groups
We shall discuss three recent results on automatic continuity of homomorphisms: 1) Every Haar-measurable homomorphism from a locally compact group to an arbitrary topological group is continuous. 2) Every homomorphism with the Baire property from an $\omega$-narrow Cech-complete topologic...
2022-01-19, godz. 16:15, Zoom
Wiesław Kubiś (Cardinal Stefan Wyszyński University in Warsaw and Institute of Mathematics of the Czech Academy of Sciences)
Abstract evolution systems, amalgamation and homogeneity
An evolution system is just a category with a distinguished class of arrows, called transitions. This concept, in particular, generalizes abstract rewriting system. It turns out that evolution systems with amalgamation provide a good framework for studying homogeneous structures, both finite and i...
