We provide a direct and elementary proof of the fact that the category of Nachbin’s compact ordered spaces is dually equivalent to an ₁ ℵ 1 -ary variety of algebras. Further, we show that ₁ ℵ 1 is a sharp bound: compact ordered spaces are not dually equivalent to any SP SP -class of finitary algebras.
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Abbadini et al. (2020) studied this question.
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