[Settfa] Tuesday 13/04, Piotr Nowakowski

[kubis at math.cas.cz]

 ------------------------------------------------------------------------- 

 Tuesday 13th April, 10:30am 
 
  Place: Zoom:

https://cesnet.zoom.us/j/93170324507?pwd=NEtINFlIUGZEQVZZMmVJOHRNNUlYQT09

 
    ------------------------------------------------------------------------- 

 Speaker:Piotr Nowakowski, IM CAS / Lodz University of Technology
 Title: Families of central Cantor sets from the category and measure viewpoints

 Abstract  

 We consider the family CS of central Cantor subsets of [0,1]. Each set in CS is uniquely determined by a sequence a=(an)belonging to the Polish space X:=(0,1)N equipped with probabilility product measure. This yields a one-to-one correspondence between sets in CS and sequences in X. We study the subfamilies H0, P0, SP, P, N and M of CS, consisting (respectively) of sets with Haudsdorff dimension 0, sets with packing dimension 0, strongly porous sets, porous sets, null sets and microscopic sets. We will examine how large,with respect to measure and Baire category, are they in CS, while we treat them as the corresponding subsets of X.

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