Polishness of some topologies related to word or tree automata

Abstract

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.

Keywords

• mathematics - logic
• computer science - formal languages and automata theory
• computer science - logic in computer science