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

Abstract

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.

26 pages; cosmetic changes, mostly