English

The dual of compact ordered spaces is a variety

Logic 2022-11-09 v3

Abstract

In a recent paper (2018), D. Hofmann, R. Neves and P. Nora proved that the dual of the category of compact partially ordered spaces and monotone continuous maps is a quasi-variety - not finitary, but bounded by 1\aleph_1. An open question was: is it also a variety? We show that the answer is affirmative. We describe the variety by means of a set of finitary operations, together with an operation of countably infinite arity, and equational axioms. The dual equivalence is induced by the dualizing object [0,1].

Keywords

Cite

@article{arxiv.1902.07162,
  title  = {The dual of compact ordered spaces is a variety},
  author = {Marco Abbadini},
  journal= {arXiv preprint arXiv:1902.07162},
  year   = {2022}
}