Weekly research seminar

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 ...

2022-11-30, 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, 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...