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## Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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# Seminarium „Topologia i teoria mnogości”

5050

## Lista referatów

• 2023-01-25, godz. 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, godz. 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, godz. 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, godz. 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, godz. 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, godz. 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 ...

• 2022-11-30, godz. 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, godz. 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...

• 2022-11-09, godz. 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, godz. 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...