Polishness of some topologies related to automata (Extended version).
Olivier Finkel, Olivier Carton, Dominique Lecomte · 2017
We prove that the B\uchi topology, the automatic topology, the alphabetic topology and the strong alphabetic topology are Polish, and provideconsequences 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.