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Cotygodniowe seminarium badawcze
2019-03-27, godz. 16:15, 5050
Jerzy Kąkol (A. Mickiewicz University)
Grothendieck spaces C(K), Efimov spaces, and the separable quotient problem for spaces C_p(X)
The abstract of the talk can be found here: http://www.mimuw.edu.pl/~wmarcisz/Seminarium/Warszawa-27-03.2019.pdf The next meeting of the seminar is planned on April 10th (there will be no meeting on April 3rd). ...
2019-03-20, godz. 16:15, 5050
Ziemowit Kostana (University of Wrocław)
On countably saturated linear orders
We will say that a linear order L is countably saturated if for any two countable subsets A,B of L, such that any element of A is less than any element of B, we can find an element of L between them. This obvious generalization of density corresponds to ”countable saturation” from model theo...
2019-03-13, godz. 16:15, 5050
Taras Banakh (Ivan Franko National University of Lviv and UJK Kielce)
Universally meager sets and the Baire category property of some function spaces
We shall discuss the problem of inner characterization of topological spaces $X$ for which the space $B_1(X)$ of real-valued Baire class one functions is Baire or Choquet. We prove that for any separable metrizable space $X$ the following implications hold: ($X$ is a $\lambda$-space)<=>($B_1(X...
2019-03-06, godz. 16:15, 5050
Piotr Szewczak (Cardinal Wyszyński University in Warsaw)
Let X be a set of reals and Cp(X) be the set of all continuous real-valued functions on X with the pointwise convergence topology. By the result of Gerlits and Nagy the space Cp(X) has the Frechet-Urysohn property (a generalization of first-countability) if and only if the set X is a gamma-set (i.e....
2019-02-27, godz. 16:15, 5050
Maciej Malicki (Warsaw School of Economics)
Complexity of the isomorphism relation for metric structures
For a given sentence s in the infinitary logic, one can consider the Borel space M of all countable models satisfying s, and the isomorphism equivalence relation E on M. Hjorth and Kechris found a natural characterization in model-theoretic terms of the situations when E is smooth or essentially cou...
2019-01-09, godz. 16:15, 5050
Mikołaj Krupski (University of Warsaw)
The functional tightness of infinite products
The functional tightness $t_0(X)$ of a space $X$ is a cardinal invariant related to both the tightness $t(X)$ and the density character $d(X)$ of $X$. While the tightness $t(X)$ measures the minimal cardinality of sets required to determine the topology of $X$, the functional tightness measures the...
2018-12-19, godz. 16:15, 5050
Mikołaj Krupski (University of Warsaw)
Games, hereditarily Baire hyperspaces and Mengerness at infinity
A topological space X is Baire if the intersection of a countable family of open dense sets in X is dense. We say that X is hereditarily Baire if every closed subspace of X is Baire. In my talk I will focus on the following problem: Let X be a separable metric space. When the hyperspace K(X) of ...
2018-12-12, godz. 16:15, 5050
Andrzej Starosolski (Silesian University of Technology)
The Rudin–Keisler ordering of P-points under b = c (a continuation)
M. E. Rudin (1971) proved, under CH, that for each P-point there exists a P-point strictly RK-greater. This result was proved under p = c by A. Blass (1973), who also showed that each RK-increasing ω-sequence of P-points is upper bounded by a P-point, and that there is an order embedding...
2018-12-05, godz. 16:15, 5050
Andrzej Starosolski (Silesian University of Technology)
The Rudin–Keisler ordering of P-points under b = c
M. E. Rudin (1971) proved, under CH, that for each P-point there exists a P-point strictly RK-greater. This result was proved under p = c by A. Blass (1973), who also showed that each RK-increasing ω-sequence of P-points is upper bounded by a P-point, and that there is an order embedding of th...
2018-11-28, godz. 16:15, 5050
Wiesław Kubiś (Cardinal Stefan Wyszyński University in Warsaw and Institute of Mathematics of the Czech Academy of Sciences)
A mathematical structure is called homogeneous if every isomorphism between its ``small" substructures extends to an automorphism. If additionally, this extension can be made algebraic, namely, preserving compositions, we then say that the structure is uniformly homogeneous. Homogeneous structures ...
