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.