February 2016

Robert Rałowski: Bernstein set and continuous functions

Tuesday, March 1, 2016 17:15

Room: D1-215

Speaker:
Robert Rałowski

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

Tuesday, February 23, 2016 17:15

Room: D1-215

Speaker:
Aleksander Cieślak

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.