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

Abstract:

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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