Olivier Finkel, Olivier Carton, Dominique Lecomte
Published 2017-10-11Version 1
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.
Comments: This paper is an extended version of a paper which appeared in the proceedings of the 26th EACSL Annual Conference on Computer Science and Logic, CSL 2017. The main addition with regard to the conference paper consists in the study of the B\"uchi topology and of the Muller topology in the case of a space of trees, which now forms Section 3.4
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