Tuesday, April 17, 2018 17:15

Room: D1-215

Speaker:

Title: Tunnels through topological spaces

Abstract. I will show a ZFC example of a compact space (without isolated points) through which one cannot drill a tunnel. I will discuss when and when not $$\omega^*$$ has a tunnel.

# Grzegorz Plebanek: Strictly positive measures on Boolean algebras

Tuesday, March 27, 2018 17:15

Room: D1-215

Speaker:
Grzegorz Plebanek

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)

Tuesday, March 13, 2018 17:15

Room: D1-215

Speaker:
Grzegorz Plebanek

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.

# Jacek Tryba: Homogeneity of ideals

Tuesday, March 6, 2018 17:15

Room: D1-215

Speaker:
Jacek Tryba

Title: Homogeneity of ideals

Abstract. The homogeneity family of the ideal $$\mathcal{I}$$ is a family of subsets such that the restriction of $$\mathcal{I}$$ to this subset is isomorphic to $$\mathcal{I}$$. We say that an ideal $$\mathcal{I}$$ is homogeneous if all $$\mathcal{I}$$-positive sets belong to the homogeneity family of $$\mathcal{I}$$. We investigate basic properties of this notion, give examples of homogeneous ideals and present some applications to ideal convergence. Moreover, we present connections between the homogeneity families and the notion of bi-$$\mathcal{I}$$-invariant functions introduced by Balcerzak, Głąb and Swaczyna and give answers to several questions related to this topic.

# Olena Karlova: Extension of Borel maps and Borel retracts of topological spaces

Tuesday, December 19, 2017 17:15

Room: D1-215

Speaker:
Olena Karlova

Title: Extension of Borel maps and Borel retracts of topological spaces

Abstract. We will discuss the problem of extension of (dis)continuous maps between topological spaces. Concepts of Baire and Borel retracts of topological spaces will be introduced. Some open problems will be considered.