# [Settfa] Tuesday 25/05, Claudio Agostini

kubis at math.cas.cz kubis at math.cas.cz
Thu May 20 21:00:03 CEST 2021

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Tuesday 25th May, 10:30am

Place: Zoom:
https://cesnet.zoom.us/j/93170324507?pwd=NEtINFlIUGZEQVZZMmVJOHRNNUlYQT09

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Speaker:Claudio Agostini, University of Turin
Title: Complete metrizability at uncountable cardinals

Abstract

In the last two decades, there has a been a rising interest in generalizing results of descriptive set theory to uncountable cardinals $\kappa$.

An open problem in the area is how to define a good class of Polish-like spaces of uncountable dimension''.

While it is true that the weight of a metric space can be an uncountable cardinal, metrizability still encloses a certain grade of countability, as every metrizable space is first countable.

This makes standard metrics unsuitable for generalized descriptive set theory, where usually the spaces taken into account have no local base of size $&lt;\kappa$.

In this talk, we are going to look at some different (new and old) natural generalizations of the concept of complete metric space that instead are suitable for this context. I will compare these classes and show that they are closely related. Finally, I will show of many results from classical descriptive set theory about Polish spaces can be extended to any of these classes.

This is a joint work with Luca Motto Ros and Philipp Schlicht.