Polishness of some topologies related to word or tree automata
Résumé
We prove that the B\"uchi topology and the automatic topology are Polish. 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 are not Polish in this case.
Mots clés
automatic topology
B\"uchi topology
finer topologies
Cantor space
B\"uchi automaton
logic in computer science
infinite words
regular $\omega$-language
Automata and formal languages
B\"uchi tree automaton
logic in computer science
Automata and formal languages
space of infinite labelled binary trees
Muller tree automaton
Polish topology
ACM Subject Classification F11 Models of Computation
F13 Complexity Measures and Classes
F41 Mathematical Logic
F43 Formal Languages Keywords and phrases Automata and formal languages
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