Polishness of some topologies related to word or tree automata - Olivier Finkel; Olivier Carton; Dominique Lecomte (Logical Methods in Computer Science, 2019)
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.