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

Jean Goubault-Larrecq, Simon Halfon, Aliaume Lopez
2022 arXiv   pre-print
We show that the spaces of transfinite words, namely 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 dimension and on its stature.
arXiv:2202.05047v2 fatcat:j5fuqiuyvrd7vhodqwjxdzqd3q