Katarzyna Chrząszcz

Katarzyna Chrząszcz: On some properties of microscopic sets

Tuesday, April 14, 2015 18:45

Room: D1-215

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  \(\varepsilon>0\) there exists a sequence of segments \((I_n)_{n\in\mathbb{N}}\) such that \(A\subseteq\bigcup\limits_{n\in\mathbb{N}} I_n\) and \(|I_n|\leq\varepsilon^n\) 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.