10.46298/dmtcs.392
https://dmtcs.episciences.org/392
Simonnet, Pierre
Pierre
Simonnet
Cagnard, Benoit
Benoit
Cagnard
Baire and automata
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 ω-rational 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.
episciences.org
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
2015-06-09
2007-01-01
2007-01-01
en
journal article
https://hal.science/hal-00966518v1
1365-8050
https://dmtcs.episciences.org/392/pdf
VoR
application/pdf
Discrete Mathematics & Theoretical Computer Science
Vol. 9 no. 2
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