Tuesday, April 14, 2015 18:45

Room: D1-215

Speaker: Katarzyna Chrząszcz

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 set  $A\subseteq \mathbb{R}$ is called microscopic if for every  $\epsilon >0$ there exists a sequence of segments $(I_n{)}_{n\in \mathbb{N}}$ such that $A\subseteq \bigcup _{n\in \mathbb{N}}{I}_n$ and $|I_n|\le {\epsilon }^n$ for $n\in \mathbb{N}$.

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.

Tags: Katarzyna Chrząszcz