Grzegorz Plebanek

# Grzegorz Plebanek: Aftermath of the Winter School

26/02/24 15:32

Tuesday, February 27, 2024 17:15

*Location:*A.4.1 C-19*Grzegorz Plebanek*

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*Title*: Aftermath of the Winter School*Abstract*: We shall discuss two problem on measures on compact spaces posed by Jiri Spurny.# Grzegorz Plebanek: Countable extensions of compact lines

09/03/23 20:47

Tuesday, March 14, 2023 17:00

*Location:*room**A.2.22 C-19***Grzegorz Plebanek*

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*Title*: Countable extensions of compact lines*Abstract*: For a compact space \(K\), we say that \(L\) is a countable discrete extension of \(K\) if \(L\) is compact and consists of \(K\) and a countable set of isolated points. We investigate some properties of such extenions for separable compact lines \(K\). This is directly related to properties of almost chains of subsets of \( \mathbb{N}\).# Grzegorz Plebanek: A complemented subspace of a C(K)-space which is not a C(K)-space

14/01/22 18:31

Tuesday, January 18, 2022 17:00

*Location:*room 605, Mathematical Institute, University of Wroclaw*Grzegorz Plebanek*

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*Title*: A complemented subspace of a C(K)-space which is not a C(K)-space*Abstract*: We present a construction of two separable compacta K and L such that C(L) is a direct sum of C(K) and some Banach space X which is not isomorphic to a space of continuous functions. Joint work with Alberto Salguero Alarcon (Badajoz).# Grzegorz Plebanek: Generalized Corson compacta and calibers of measures

08/11/21 16:45

Tuesday, November 9, 2021 17:00

*Location:*room 605, Mathematical Institute, University of Wroclaw*Grzegorz Plebanek*

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*Title*: Generalized Corson compacta and calibers of measures*Abstract*: We consider compact spaces which can be embedded into a product of real lines so that the support of every element is of size \(<\kappa\); here \(\kappa\) is a fixed cardinal number. We discuss measure-theoretic properties of such spaces and related properties of Banach spaces of continuous functions.# Grzegorz Plebanek: A connected version of Kunen's compact L-space

20/01/21 16:57

Tuesday, January 26, 2021 17:00

*Location:***Zoom.us**: if you want to participate please contact organizers*Grzegorz Plebanek*

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*Title*: A connected version of Kunen's compact L-space*Abstract*: Modifying Kunen's construction from 1981, we show that under CH there is a compact connected space K that carries a regular normal probability measure (normal = `all Borel sets with empty interior have measure zero'). Then we show that the Banach space C(K) of continuous functions is isomorphic to no space of the form C(L) with L compact and zero-dimensional.# Grzegorz Plebanek: Baire Category Theorem in \(\mathbb{R}^\kappa\)

16/01/20 07:51

Tuesday, January 21, 2020 17:15

*Room:*D1-215*Grzegorz Plebanek*

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*Title*: Baire Category Theorem in \(\mathbb{R}^\kappa\)*Abstract*. A topological space X is BAIRE if it satisifes the theorem in the title. The space X is hereditary Baire if every closed subspace of X is Baire. We discuss a question which products of the real lines are hereditary Baire.# Grzegorz Plebanek: Small almost disjoint families with applications

19/05/19 22:16

Tuesday, May 21, 2019 17:15

*Room:*D1-215*Grzegorz Plebanek*

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*Title*: Small almost disjoint families with applications*Abstract*. We consider almost disjoint families that cannot be divided into n separated parts (for a fixed n). The basic question is what is the possible size of such a family. Those families are applicable to some problems on spaces of continuous functions.# Grzegorz Plebanek: Strictly positive measures on Boolean algebras

20/03/18 21:43

Tuesday, March 27, 2018 17:15

It turns out that the positive answer follows from the existence of some large cardinals, while the counterexample can be found in the model of \(V=L\).

*Room:*D1-215*Grzegorz Plebanek*

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*Title*: Strictly positive measures on Boolean algebras*Abstract*. \(SPM\) denotes the class of Boolean algebras possessing strictly positive measure (finitely additive and probabilistic). Together with Menachem Magidor, we consider the following problem: Assume that \(B\) belongs to \(SPM\) for every subalgebra \(B\) of a given algebra \(A\) such that \(|B|\le\mathfrak c\). Does it imply that the algebra \(A\) belongs to \(SPM\)?It turns out that the positive answer follows from the existence of some large cardinals, while the counterexample can be found in the model of \(V=L\).

# Grzegorz Plebanek: On almost disjoint families with property (R)

07/03/18 21:13

Tuesday, March 13, 2018 17:15

*Room:*D1-215*Grzegorz Plebanek*

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*Title*: On almost disjoint families with property (R)*Abstract*. We consider (with A.Aviles and W. Marciszewski) almost disjoint families with some combinatorial property that has applications in functional analysis. We are looking for the minimal cardinality of m.a.d. family with property (R). It turns out that this cardinal is not greater than \(non(\mathcal{N})\) the uniformity of null sets.# Grzegorz Plebanek: About a particular measure on the square

13/12/14 03:14

Tuesday, December 16, 2014 17:15

*Room:*D1-215*Grzegorz Plebanek*

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*Title*: About a particular measure on the square*Abstract*. Assuming the existence of SierpiĆski set we construct a measure on some \(\sigma\)-field of subsets of the square which is perfect but not compact. This construction in 2001 answered Fremlin's question. We will describe open problems connected to this field.