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

Abstract

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 dimension and on its stature.