December 2014

# 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*

Speaker:Speaker:

*Title*: About a particular measure on the square*Abstract*. Assuming the existence of Sierpiński 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.# Robert Rałowski: On generalized Luzin sets

05/12/14 18:34

Tuesday, December 9, 2014 17:15

*Room:*D1-215*Robert Rałowski*

Speaker:Speaker:

*Title*: On generalized Luzin sets*Abstract*. We will show results obtained together with Sz. Żeberski concerning properties of \((I,J)\)-Luzin sets (for \(I, J\) \(\sigma\)-ideals on Polish space). Under some settheoretical assumptions we will construct \(\mathfrak{c}\) many generalized Luzin sets which are not Borel equivalent. We will also examine some forcing notions which do not kill generalized Luzin sets.# Piotr Drygier: Compactifications of \(\omega\) with strictly positive measure

01/12/14 01:49

Tuesday, December 2, 2014 17:15

*Room:*D1-215*Piotr Drygier*

Speaker:Speaker:

*Title*: Compactifications of \(\omega\) with strictly positive measure*Abstract*. Under certain axioms related to cardinal invariants we will show the construction of compactification of natural numbers, which reminder is a non-separable space having a strictly positive measure. In addition, we will discuss consequences of given result to complementarity of \(c_0\) in the space of continuous functions.