Two Effective Properties of ω-Rational Functions

We prove two new effective properties of rational functions over infinite words which are realized by finite state Büchi transducers. Firstly, for each such function [Formula: see text], one can construct a deterministic automaton text] accepting dense text]-subset that the restriction to is continuous. Secondly, we give proof decidability first Baire class synchronous text]-rational from get an extension this result involving notion Wadge classes regular text]-languages.