🔬 Research > Journals

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

  Jean Goubault-Larrecq, Simon Halfon, Aliaume Lopez

  Published at Colloquium Mathematicum

  [arXiv] [doi] [hal]

  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.