The interplay between topology and automata theory has a form of synergy: descriptive set theory motivates new problems and methods in automata theory but on the other hand, automata theory introduces natural examples for classical topological concepts.

During this talk I will introduce basic notions of topology and descriptive set theory focusing on the case of infinite words. I’ll say what is the Borel hierarchy and the Wadge order. Then I’ll show how these tools are related to automata theory. I’ll try to argue that even from purely automata theoretic point of view, it is possible to obtain new results and new proofs by referring to topological concepts.