December 2014

# Grzegorz Plebanek: About a particular measure on the square

Tuesday, December 16, 2014 17:15

Room: D1-215

Speaker:
Grzegorz Plebanek

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

Tuesday, December 9, 2014 17:15

Room: D1-215

Speaker:
Robert Rałowski

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

Tuesday, December 2, 2014 17:15

Room: D1-215

Speaker:
Piotr Drygier

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.