Ondrej Zindulka: Microscopic sets, Hausdorff measures and their cardinal invariants
04/05/22 19:27
Monday, May 9, 2022 15:15
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Ondrej Zindulka (Czech Technical University, Prague)
Title: Microscopic sets, Hausdorff measures and their cardinal invariants
Abstract: A set in a metric space is microscopic it admits, for every \(\varepsilon>0\), a cover \(\{E_n\}\) such that the diameter of each \(E_n\) is at most \(\varepsilon^n\). The notion was introduced 21 years ago and since then a number of people contributed to the theory. I will provide a brief account of the state of art and present new results and in particular the so far overlooked relation to Hausdorff measures. Attention will be paid to cardinal invariants of the ideal of microscopic sets and sets of Hausdorff measure zero in metric spaces and Polish groups.
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Ondrej Zindulka (Czech Technical University, Prague)
Title: Microscopic sets, Hausdorff measures and their cardinal invariants
Abstract: A set in a metric space is microscopic it admits, for every \(\varepsilon>0\), a cover \(\{E_n\}\) such that the diameter of each \(E_n\) is at most \(\varepsilon^n\). The notion was introduced 21 years ago and since then a number of people contributed to the theory. I will provide a brief account of the state of art and present new results and in particular the so far overlooked relation to Hausdorff measures. Attention will be paid to cardinal invariants of the ideal of microscopic sets and sets of Hausdorff measure zero in metric spaces and Polish groups.