Polishness of Some Topologies Related to Automata

Olivier Carton (1) , Olivier Finkel (2) , Dominique Lecomte (2)

1 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

We prove that the Büchi topology, the automatic topology, the alphabetic topology and the strong alphabetic topology are Polish, and provide consequences of this.

Mots clés: Automata and formal languages; logic in computer science; infinite words; Büchi automaton; regular ω-language; Cantor space; finer topologies; Büchi topology; automatic; topology; alphabetic topology; strong alphabetic topology; Polish topology

Domaines: Logique [math.LO]

Olivier Carton, Olivier Finkel, Dominique Lecomte. Polishness of Some Topologies Related to Automata. 26th EACSL Annual Conference on Computer Science and Logic (CSL 2017), Aug 2017, Stockholm, Sweden. pp.22:1-22:16, ⟨10.4230/LIPIcs.CSL.2017.22⟩. ⟨hal-01590185⟩