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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