Weekly research seminar

2023-06-14, 16:15, 5050

Jakub Andruszkiewicz (Doctoral School of Exact and Natural Sciences UW)

**Cofinalities of the symmetric group and of the ultrapowers of ω**We consider the following cardinal invariants of the continuum: cf(Sym(ω)), being the cofinality of the group of permutations of ω, and mcf, defined as the minimal cofinality of an ultrapower of ω over any non-principal ultrafilter. During the talk we will present known results regarding the rela...

2023-05-31, 16:15, 5050

Piotr Koszmider (IM PAN)

**Ramsey properties of the distance on nonseparable spheres**Given a nonseparable metric space (M,d) bounded by 2 we consider (A) dichotomies D_r for r in (0,2): either there is uncountable subset N of M such that d(x, y) > r for all distinct x,y in N or else M is the union of countably many sets each of diameter not bigger than r; (B) the metric...

2023-05-24, 16:15, 5050

Grzegorz Plebanek (University of Wrocław)

**Countable discrete extensions of compact lines**We consider a separable compact line K and its extension L consisting of K and a countable number of isolated points. The main object of study is the existence of a bounded extension operator E: C(K) -> C(L). We show that if such an operator exists then there is one which norm is an odd natural n...

2023-05-10, 16:15, Zoom

Aristotelis Panagiotopoulos (Carnegie Mellon University)

**Menger continua via projective Fraïssé theory**Projective Fraïssé theory was introduced by T.Irwin and S.Solecki as a natural framework for analyzing the dynamics of homeomorphism groups of compact metrizable spaces in terms of finite combinatorics. In this talk I will provide some basic background in projective Fraïssé t...

2023-04-26, 16:15, 5050

Jarosław Swaczyna (Lodz University of Technology)

**Continuity of coordinate functionals for ideal Schauder basis**Given an ideal of subsets of natural numbers I we say that a sequence (x_n) is I-convergent to x if for every ε>0 condition {n \in N:d(x_n,x)>ε}\in I holds. We may use this notion to generalize the idea of Schauder basis, namely we say that a sequence (e_n) is an I-basis if for every x \in X there...

2023-04-19, 16:15, 5050

Tomasz Weiss (Cardinal Stefan Wyszyński University in Warsaw)

**Countably perfectly meager and countably perfectly null sets**We study a strengthening of the notion of a universally meager set and its dual counterpart that strengthens the notion of a universally null set. We say that a subset A of a perfect Polish space X is countably perfectly meager (respectively, countably perfectly null) in X, if for every perfec...

2023-03-29, 16:15, 5050

Daria Michalik (University of Warsaw)

**Blocking properties of the diagonal in Cartesian product**The abstract of the talk can be found on the webpage of our seminar: https://www.mimuw.edu.pl/en/seminaria/topology-and-set-theory-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...