Katarzyna Chrząszcz: On some properties of microscopic sets

Tuesday, April 14, 2015, 18:45
Wrocław University of Technology, 215 D-1

Speaker: Katarzyna Chrząszcz (Technical University of Łódź)

Title: On some properties of microscopic sets


The notion of microscopic set appeared for the first time in paper ‘Insiemi ed operatori “piccoli” in analisi funzionale’ (APPELL, J., Rend. Istit. Mat. Univ. Trieste 33 (2001), 127–199).

Def. A subset A of reals is called microscopic if for every e>0 there exists a sequence of segments (I_n)_{nin N} such that A is covered by the union of I_n’s and the length of I_n is less or equal to e^n for every n.

We will give generalizations of given notion to the case of arbitrary metric space. We will analyze algebraic and set-theoretic properties of the family of microscopic sets.

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