Weekly research seminar
Organizers
 prof. dr hab. Witold Marciszewski
 prof. dr hab. Piotr Zakrzewski
Information
Wednesdays, 4:15 p.m. , room: 5050Research fields
List of talks

May 22, 2024, 4:15 p.m.
Lyubomyr Zdomskyy (Technische Universit¨at Wien)
Countable spaces, realcompactness, and cardinal characteristics.
In this talk we shall analyze the realcompactness number of countable spaces. In particular, we plan to show that for a cardinal \kappa, there exists a countable Tychonoff space X without isolated points such that …

May 15, 2024, 4:15 p.m.
Grzegorz Plebanek (University of Wrocław)
Complemented subspaces of C(K x L)
We prove that whenever K and L are nonscattered compacta then the Banach space C(K x L) contains a complemented copy of C[0,1]. This is joint work with Jakub Rondos and Damian Sobota.

May 8, 2024, 4:15 p.m.
Piotr BorodulinNadzieja (University of Wrocław)
Pmeasures in models without Ppoints
I will discuss the existence of Pmeasures (a Pmeasure is an analog of the notion of Ppoint in the realms of finitely additive measures on omega) in the models without Ppoints. In particular I will …

April 24, 2024, 4:15 p.m.
Krzysztof Zakrzewski (Doctoral School of Exact and Natural Sciences UW)
Function spaces on Corsonlike compacta
Recall that a compact space is Eberlein compact if it is homeomorphic to a subspace of some Banach space equipped with the weak topology. A compact space is \omegaCorson compact if it embeds into a …

April 17, 2024, 4:15 p.m.
Jakub Andruszkiewicz (Doctoral School of Exact and Natural Sciences UW)
Existence of many finitely generated precompact subgroups of G and L_0(G)
For a Polish group G one can define L_0(G) as the set of all (Borel or) Lebesgue measurable functions from [0,1] to G. This set, after identifying functions that are equal up to a set …

April 10, 2024, 4:15 p.m.
Kacper Kucharski (Doctoral School of Exact and Natural Sciences UW)
On property (B) in function spaces
A topological space Z has the property (B) of Banakh if there exists a countable family of closed nowhere dense subsets of Z that absorbs all compact subsets of Z, i.e., each compact subset of …

March 20, 2024, 4:15 p.m.
Piotr Zakrzewski (UW)
On two consequences of CH established by Sierpiński, part 2
We study the relations between two consequences of the Continuum Hypothesis discovered by Wacław Sierpiński, concerning uniform continuity of continuous functions and uniform convergence of sequences of realvalued functions, defined on uncountable subsets of the …

March 13, 2024, 4:15 p.m.
Piotr Zakrzewski (UW)
On two consequences of CH established by Sierpiński
We study the relations between two consequences of the Continuum Hypothesis discovered by Wacław Sierpiński, concerning uniform continuity of continuous functions and uniform convergence of sequences of realvalued functions, defined on uncountable subsets of the …

March 6, 2024, 4:15 p.m.
Kamil Ryduchowski
Lusin sets and uncountable Auerbach systems
Hajek, Kania and Russo showed that under CH there is an equivalent renorming of the Banach space c_0(omega_1) without uncountable Auerbach systems. It is not known whether extra settheoretic assumptions can be dropped here. During …

Feb. 28, 2024, 4:15 p.m.
Robert Simon
Paradoxical colouring rules
A colouring rule is a way to determine a function from a probability space to a set of colours based on the colours of finitely many measure preserving transformations. It is paradoxical if there is …

Jan. 24, 2024, 4:15 p.m.
Taras Banakh (Ivan Franko National University of Lviv and UJK Kielce)
Strongly rigid countable Hausdorff spaces
A topological space $X$ is strongly rigid if every noidentity continuous selfmap of $X$ is constant. Among known examples of strongly rigid spaces one can recall the famous Cook continua. In fact, every strongly rigid …

Jan. 10, 2024, 4:15 p.m.
Piotr Szewczak (Cardinal Stefan Wyszyński University in Warsaw)
Concentrated sets in the Miller model
A set of reals X is concentrated if it is uncountable and there is a countable subset D of X such that for each open set U containing D the set X\U is countable. Using …

Dec. 20, 2023, 4:15 p.m.
Zdeněk Silber (IM PAN)
K) space admitting a nonseparable measur
In the talk we focus on the relation of countable tightness of the space P(K) of Radon probabilty measures on a compact Hausdorff space K and of existence of measures in P(K) that have uncountable …

Dec. 13, 2023, 4:15 p.m.
Maciej Malicki (IM PAN)
Compacta and their homeomorphism groups from posets, part 2
Very recently A. Bartoš, T. Bice and A. Vignati discovered a duality, generalizing the Stone duality, between second countable T_1 compacta and graded omegaposets. Their approach allows for elementary combinatorial constructions, in the spirit of …

Dec. 6, 2023, 4:15 p.m.
Adam Bartoš ("An introduction to abstract Fraïssé theory") and Wiesław Kubiś ("Uncountable homogeneous structures") (Institute of Mathematics of the Czech Academy of Sciences)
"An introduction to abstract Fraïssé theory" and "Uncountable homogeneous structures"
"An introduction to abstract Fraïssé theory": We give a gentle introduction to abstract countable discrete Fraïssé theory. First, we recall three classical examples of ultrahomogeneous structures: the linear order of the rationals, the random graph, …