Polishness of some topologies related to automata (Extended version)

10/11/2017
by   Olivier Finkel, et al.
0

We prove that the Büchi 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 Büchi and the Muller topologies in that case are not Polish.

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