5 citations · 8 across the 6 of their papers we have counts for
4 papers · 1 filter
Fixed Points and Noetherian Topologies
Aliaume Lopez
This paper provides a canonical construction of a Noetherian least fixed point topology. While such least fixed point are not Noetherian in general, we prove that under a mild assu…
Z-polyregular functions
Thomas Colcombet, Gaëtan Douéneau-Tabot, Aliaume Lopez
This paper introduces a robust class of functions from finite words to integers that we call Z-polyregular functions. We show that it admits natural characterizations in terms of l…
When Locality Meets Preservation
Aliaume Lopez
This paper investigates the expressiveness of a fragment of first-order sentences in Gaifman normal form, namely the positive Boolean combinations of basic local sentences. We show…
Infinitary Noetherian Constructions II. Transfinite Words and the Regular Subword Topology
Jean Goubault-Larrecq, Simon Halfon, Aliaume Lopez
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…