The dual of compact ordered spaces is a variety

Marco Abbadini

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arXiv · 1902.07162

The dual of compact ordered spaces is a variety

Marco Abbadini

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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 $\aleph_1$. 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].

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BibTeX RIS

Marco Abbadini. 2019-02-19. The dual of compact ordered spaces is a variety. https://arxiv.org/abs/1902.07162

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