Polishness of some topologies related to automata (Extended version)
Résumé
We prove that the B\"uchi topology, the automatic topology, the alphabetic topology and the strong alphabetic topology are Polish, and provide
consequences of this. We also show that this cannot be fully extended to the case of a space of infinite labelled binary trees; in particular the B\"uchi and the Muller topologies in that case are not Polish.
Mots clés
infinite words
logic in computer science
B\"uchi automaton
regular $\omega$-language
finer topologies
Cantor space
B\"uchi topology
automatic topology
alphabetic topology
B\"uchi tree automaton
Automata and formal languages
Automata and formal languages
logic in computer science
strong alphabetic topology
space of infinite labelled binary trees
Polish topology
Muller tree automaton
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