# Robert Rałowski: Bernstein set and continuous functions

Tuesday, March 1, 2016, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Robert Rałowski (Wrocław University of Technology)

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.