Weekly research seminar

2023-10-11, 16:15, 5050

Jesús M. F. Castillo (Universidad de Extremadura)

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...