[Settfa] Tuesday 01/03, Piotr Nowakowski

[kubis at math.cas.cz]

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 Tuesday 1st March, 10:00am 
 
  Place: IM in konírna 

 
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 Speaker:Piotr Nowakowski, University of Lodz, Poland
 Title: On the difference set of a central Cantor set

 Abstract  

 Let $C(\lambda )\subset [0,1]$ denote the central Cantor set generated by a sequence $\lambda =(\lambda _{n})\in (0,\frac{1}{2}) ^{\mathbb{N}}$. By the known trichotomy, the difference set $C(\lambda )-C(\lambda )$ of $C(\lambda )$ is one of three possible sets: a finite union of closed intervals, a Cantor set, or a Cantorval. Our main result describes effective conditions for $(\lambda _{n})$ which guarantee that $C(\lambda )-C(\lambda )$ is a Cantorval. We show that these conditions can be expressed in several equivalent forms. We give an application of the proved theorems for the achievement sets of some fast convergent series.

 For more information see the seminar web page at 
 https://calendar.math.cas.cz/set-theory-and-analysis-actual .