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Cotygodniowe seminarium badawcze
2018-05-09, godz. 16:15, 5050
Rafał Filipów (University of Gdańsk)
Ideal convergence versus matrix summability
Ideal convergence and matrix summability are examples of extensions of the ordinary convergence of sequences of reals to a larger class of sequences (i.e. ordinary convergent sequences remain convergent to the same limits and there are ordinary divergent sequences that are convergent in these new me...
2018-04-25, godz. 16:15, 5050
Andrzej Szymański (Cardinal Stefan Wyszyński University in Warsaw)
2018-04-11, godz. 16:15, 5050
Roman Pol (University of Warsaw)
An abelian topological group H is (Pontrjagin) reflexive if the natural homomorphism from H into the group H^^ of characters on the group of characters on H is a homeomorphism of H onto H^^ (as in the celebrated Pontrjagin duality theorem for LCA groups). All direct products Z^kappa of the addit...
2018-03-21, godz. 16:15, 5050
Piotr Szewczak (Cardinal Stefan Wyszyński University in Warsaw)
An old problem asks whether every compact group has a Haar-nonmeasurable subgroup. A series of earlier results reduce the problem to infinite metrizable profinite groups. We provide a positive answer, assuming a weak, potentially provable, consequence of the Continuum Hypothesis. We also establish t...
2018-03-14, godz. 16:15, 5050
Ralf Schindler (Department for Mathematical Logic and Foundational Research, University of Munster)
"Paradoxical" sets with no well-ordering of the reals
By a Hamel basis we mean a basis for the reals, R, construed as a vecor space over the field of rationals. In 1905, G. Hamel constructed such a basis from a well-ordering of R. In 1975, D. Pincus and K. Prikry asked "whether a Hamel basis exists in any model in which R cannot be well ordered.&q...
2018-03-07, godz. 16:15, 5050
Witold Marciszewski (University of Warsaw)
On zero-dimensional subspaces of Eberlein compacta
Let us recall that a compact space K is Eberlein compact if it can be embedded into some Banach space X equipped with the weak topology. We will discuss the following problem: Does every nonmetrizable Eberlein compact space contain a closed zero-dimensional, nonmetrizable subspace? We will cons...
2018-02-28, godz. 16:15, 5050
TOMASZ NATKANIEC (University of Gdańsk)
PERFECTLY EVERYWHERE SURJECTIVE BUT NOT JONES FUNCTIONS
Given a function f : R → R we say that • f is perfectly surjective (f ∈ PES) if f[P] = R for every perfect set P; • f is a Jones function (f ∈ J) if C ∩ f is non-empty for every closed C ⊂ R^2 with dom(C) of size c. M. Fenoy-Munoz, J.L. Gamez-Merino, G.A. Munoz-Fernandez a...
2018-01-24, godz. 16:15, 5050
Taras Banakh (Lviv National University and UJK Kielce)
Null-finite sets in metric groups and their applications
We shall introduce a new family of "small" sets which is tightly connected with two well known $\sigma$-ideals: of Haar-null sets and of Haar-meager sets. We define a subset $A$ of a topological group $X$ to be null-finite if there exists an infinite compact subset $K\subset X$ such that for every $...
2018-01-17, godz. 16:15, 5050
Szymon Żeberski (Wrocław University of Technology)
Nonmeasurable sets and unions with respect to tree ideals
We consider a notion of nonmeasurablity with respect to Marczewski and Marczewski-like tree ideals $s_0$, $m_0$, $l_0$, and $cl_0$. We show that there exists a subset $A$ of the Baire space $\omega^\omega$ which is $s$-, $l$-, and $m$-nonmeasurable, that forms dominating m.a.d. family. We introduce ...
2017-12-20, godz. 16:15, 5050
Damian Sobota (Kurt Gödel Research Center for Mathematical Logic)
Convergence of measures and cardinal characteristics of the continuum
Let A be a Boolean algebra. We say that A has the Nikodym property if every pointwise convergent sequence of measures on A is weak* convergent. Similarly, A has the Grothendieck property if every weak* convergent sequence of measures on A is weakly convergent (equivalently: convergent on every B...
