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Weekly research seminar
2023-03-22, 16:15, Zoom
Taras Banakh (Ivan Franko National University of Lviv and UJK Kielce)
An example of a 36-Shelah group
A group $G$ is called $n$-Shelah if $G=A^n$ for any subset $A\subseteq G$ of cardinality $|A|=|G|$. In 1980 Saharon Shelah constructed his famous CH-example of an uncountable 6640-Shelah group. This group was the first example of a nontopologizable group. On the other hand, by a result of Protasov, ...
2023-03-15, 16:15, 5050
Wiesław Kubiś (Akademia Nauk Republiki Czeskiej)
Ultrametric homogeneous structures
We shall present the theory of homogeneous Polish ultrametric structures. Our starting point is a Fraı̈ssé class of finite structures and the crucial tool is the universal homogeneous epimorphism. The new Fraı̈ssé limit is an inverse limit, nevertheless its universality is with respect to embe...
2023-03-08, 16:15, 5050
Zdeněk Silber (IM PAN)
The weak* derived set of a subset A of a dual Banach space X* is the set of weak* limits of bounded nets in A. It is known that a convex subset of a dual Banach space is weak* closed if and only if it equals its weak* derived set. But this does not mean that the weak* closure of a convex set coincid...
2023-03-01, 16:15, 5050
Adam Kwela (University of Gdańsk)
Katětov order and its applications
This talk is an overview of my recent articles on ideals on countable sets. I will present set-theoretic and topological applications of Katětov order on ideals, focusing on distinguishing certain classes of sequentially compact spaces and comparing certain classes of ultrafilters with the class of...
2023-01-25, 16:15, 5050
Kamil Ryduchowski (Doctoral School of Exact and Natural Sciences UW)
On antiramsey colorings of uncountable squares and geometry of nonseparable Banach spaces
A subset Z of a Banach space X is said to be r-equilateral (r-separated) if every two distinct elements of Z are in the distance exactly (at least) r from each other. We will address the question of the existence of uncountable equilateral and (1 + e)-separated sets (e > 0) in the unit spheres ...
2023-01-18, 16:15, 5050
Piotr Szewczak (Cardinal Stefan Wyszyński University in Warsaw)
Totally imperfect Menger sets: Part 2
A set of reals X is Menger if for any countable sequence of open covers of X one can pick finitely many elements from every cover in the sequence such that the chosen sets cover X. Any set of reals of cardinality smaller than the dominating number d is Menger and there is a non-Menger set of cardina...
2023-01-11, 16:15, 5050
Piotr Szewczak (Cardinal Stefan Wyszyński University in Warsaw)
A set of reals X is Menger if for any countable sequence of open covers of X one can pick finitely many elements from every cover in the sequence such that the chosen sets cover X. Any set of reals of cardinality smaller than the dominating number d is Menger and there is a non-Menger set of cardina...
2022-12-21, 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, 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, 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 ...
