%0 Journal Article
%T Baire and automata
%A Benoit Cagnard
%A Pierre Simonnet
%J Discrete Mathematics & Theoretical Computer Science
%D 2007
%I Discrete Mathematics & Theoretical Computer Science
%X In his thesis Baire defined functions of Baire class 1. A function f is of Baire class 1 if it is the pointwise limit of a sequence of continuous functions. Baire proves the following theorem. A function f is not of class 1 if and only if there exists a closed nonempty set F such that the restriction of f to F has no point of continuity. We prove the automaton version of this theorem. An ¦Ø-rational function is not of class 1 if and only if there exists a closed nonempty set F recognized by a B¨¹chi automaton such that the restriction of f to F has no point of continuity. This gives us the opportunity for a discussion on Hausdorff's analysis of ¦¤¡ã 2, ordinals, transfinite induction and some applications of computer science.
%U http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/676