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## Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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# Topology and Set Theory Seminar

Weekly research seminar

5050

## List of talks

• 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)

Weak* derived sets

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)

Totally imperfect Menger sets

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)

Overcomplete sets

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)

Renormings of c_0(Γ)

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 ...