Infinitary Noetherian constructions II. Transfinite words and the regular subword topology
Volume 173 / 2023
Colloquium Mathematicum 173 (2023), 227-250
MSC: Primary 54G99; Secondary 06A07.
DOI: 10.4064/cm8793-3-2023
Published online: 12 June 2023
Abstract
We show that the space of transfinite words, that is, ordinal-indexed 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.
