Automata, Borel functions and real numbers in Pisot base
This note is about functions ƒ : whose graph is recognized by a Büchi finite automaton on the product alphabet . These functions are Baire class 2 in the Baire hierarchy of Borel functions and it is decidable whether such function are continuous or not. In 1920 W. Sierpinski showed that a function is Baire class 1 if and only if both the overgraph and the undergraph of are . We show that such characterization is also true for functions on infinite words if we replace the real ordering by the...