Robert Rałowski: Bernstein set and continuous functions
25/02/16 15:41
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.
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.