Infinitary Noetherian Constructions II. Transfinite Words and the Regular Subword Topology

Jean Goubault-Larrecq (1) , Simon Halfon (2) , Aliaume Lopez (1, 3)

1 LMF - Laboratoire Méthodes Formelles
2 CB - CB - Centre Borelli - UMR 9010
3 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale

We show that the spaces of transfinite words, namely ordinalindexed words, over a Noetherian space, is also Noetherian, under a natural topology which we call the regular subword topology. We characterize its sobrification and its specialization ordering, and we give an upper bound on its sobrification rank and on its stature.

Keywords: Noetherian spaces; well-quasi-orders; infinite words

Domains: General Topology [math.GN]; Logic in Computer Science [cs.LO]

Jean Goubault-Larrecq, Simon Halfon, Aliaume Lopez. Infinitary Noetherian Constructions II. Transfinite Words and the Regular Subword Topology. Colloquium Mathematicum, 2023, 173 (2), pp.227-250. ⟨10.4064/cm8793-3-2023⟩. ⟨hal-04283731⟩