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## Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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# Seminarium „Topologia i teoria mnogości”

5050

## Lista referatów

• 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)<=>($B_1(X... • 2019-03-06, godz. 16:15, 5050 Piotr Szewczak (Cardinal Wyszyński University in Warsaw) Products of gamma-sets Let X be a set of reals and Cp(X) be the set of all continuous real-valued functions on X with the pointwise convergence topology. By the result of Gerlits and Nagy the space Cp(X) has the Frechet-Urysohn property (a generalization of first-countability) if and only if the set X is a gamma-set (i.e.... • 2019-02-27, godz. 16:15, 5050 Maciej Malicki (Warsaw School of Economics) Complexity of the isomorphism relation for metric structures For a given sentence s in the infinitary logic, one can consider the Borel space M of all countable models satisfying s, and the isomorphism equivalence relation E on M. Hjorth and Kechris found a natural characterization in model-theoretic terms of the situations when E is smooth or essentially cou... • 2019-01-09, godz. 16:15, 5050 Mikołaj Krupski (University of Warsaw) The functional tightness of infinite products The functional tightness$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)

Uniform homogeneity

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 ...

• 2018-11-21, godz. 16:15, 5050

Grzegorz Plebanek (University of Wrocław)

On Cartesian products of compact lines

This is joint work with Gonzalo Martinez Cervantes. By a compact line we mean a compact space which topology is defined by a linear order. Answering a problem posed by Mardesic, we show that n-fold product of compact lines cannot be continuously mapped onto a product of n+1 nonmetrizable spaces. ...