We provide a direct and elementary proof of the fact that the category of Nachbin's compact ordered spaces is dually equivalent to an N-1-ary variety of algebras. Further, we show that N-1 is a sharp bound: compact ordered spaces are not dually equivalent to any SP-class of finitary algebras.
On the Axiomatisability of the Dual of Compact Ordered Spaces / M. Abbadini, L. Reggio. - In: APPLIED CATEGORICAL STRUCTURES. - ISSN 0927-2852. - 28:6(2020), pp. 921-934. [10.1007/s10485-020-09604-y]
On the Axiomatisability of the Dual of Compact Ordered Spaces
M. Abbadini;
2020
Abstract
We provide a direct and elementary proof of the fact that the category of Nachbin's compact ordered spaces is dually equivalent to an N-1-ary variety of algebras. Further, we show that N-1 is a sharp bound: compact ordered spaces are not dually equivalent to any SP-class of finitary algebras.
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