The dual of compact ordered spaces is a variety

Marco Abbadini

In a recent paper (2018), D. Hofmann, R. Neves and P. Nora proved that the dual of the category of compact 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].

Keywords: compact ordered space, variety, duality, axiomatizability

2010 MSC: Primary: 03C05. Secondary: 08A65, 18B30, 18C10, 54A05, 54F05

Theory and Applications of Categories, Vol. 34, 2019, No. 44, pp 1401-1439.

Published 2019-12-09.

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