Frucht’s theorem in Borel setting

Frucht’s theorem in Borel setting

In this paper, we show that Frucht’s theorem holds in Borel setting. More specifically, we prove that any standard Borel group can be realized as the Borel automorphism group of a Borel graph. A slight modification of our construction also yields the following result in topological setting: Any Poli...

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Veröffentlicht in:Periodica mathematica Hungarica 2024-03, Vol.88 (1), p.59-67
Hauptverfasser: Bilge, Onur, Kaya, Burak
Format: Artikel
Sprache:eng
Schlagworte:
Automorphisms
Mathematics
Mathematics and Statistics
Theorems
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Zusammenfassung:In this paper, we show that Frucht’s theorem holds in Borel setting. More specifically, we prove that any standard Borel group can be realized as the Borel automorphism group of a Borel graph. A slight modification of our construction also yields the following result in topological setting: Any Polish group can be realized as the homeomorphic automorphism group of a Σ 2 0 -graph on a Polish space.
ISSN:0031-5303
1588-2829
DOI:10.1007/s10998-023-00537-2