February 2016

# Robert Rałowski: Bernstein set and continuous functions

25/02/16 15:41

Tuesday, March 1, 2016 17:15

We show some consistency results for completely nonmeasurable sets with respect to \(\sigma\)-ideals of null sets and meager sets on the real line.

These results was obtained commonly with Jacek Cichoń, Michał Morayne and me.

*Room:*D1-215*Robert Rałowski*

Speaker:Speaker:

*Title*: Bernstein set and continuous functions*Abstract*. Alexander V. Osipov asked "It is true that for any Bernstein subset \(B\subset \mathbb{R}\) there are countable many continous functions from \(B\) to \(\mathbb{R}\) such that the union of images of \(B\) is a whole real line \(\mathbb{R}\)". We give the positive answer for this question, but we show that this result is not true for a \(T_2\) class of functions.We show some consistency results for completely nonmeasurable sets with respect to \(\sigma\)-ideals of null sets and meager sets on the real line.

These results was obtained commonly with Jacek Cichoń, Michał Morayne and me.

# Aleksander Cieślak: Filters and sets of Vitali's type

19/02/16 18:43

Tuesday, February 23, 2016 17:15

*Room:*D1-215*Aleksander Cieślak*

Speaker:Speaker:

*Title*: Filters and sets of Vitali's type*Abstract*. In construction of classical Vitali set on \(\{0,1\}^{\omega}\) we use filter of cofinite sets to define rational numbers. We replece cofinite filter by any nonprincipal filter on \(\omega\) and ask some questions about measurability and cardinality of selectors and equevalence classes.