“Smallness” on the real line.

Fecha: Del 7 de Abril al 9 de Abril de 2019.
Abstract:
The main aim of the lectures is to consider analogies between topological and measure spaces using notions of “smallness” in a sense of measure and category. a notion of sigma ideal, examples of such familes in a context of measure and category different meaning of “smallness” on the real line Cantor, Baire and Borel theorems, connections between them and examples of their usage for “existence proofs” properties of the set of Liouville numbers.