episciences.org_392_20230402143717937
20230402143717937
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Discrete Mathematics & Theoretical Computer Science
13658050
01
01
2007
Vol. 9 no. 2
Baire and automata
Pierre
Simonnet
Benoit
Cagnard
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 ωrational function is not of class 1 if and only if there exists a closed nonempty set F recognized by a Büchi 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 Δ°2, ordinals, transfinite induction and some applications of computer science.
01
01
2007
392
https://hal.science/hal00966518v1
10.46298/dmtcs.392
https://dmtcs.episciences.org/392

https://dmtcs.episciences.org/392/pdf

https://dmtcs.episciences.org/392/pdf