More on Compact Hausdorff Spaces and Finitary Duality Academic Article uri icon

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abstract

  • It is an old conjecture by P. Bankston that the category CompHaus of compact Hausdorff spaces and their continuous maps is not dually equivalent to any elementary P-class of finitary algebras (taken as a category with all homomorphisms between its members as maps), where elementary means defined by first order axioms, and a P-class is one closed under arbitrary (cartesian) products. One motivation for this conjecture is the fact that such a dual equivalence would make ultracopowers of compact Hausdorff spaces correspond to ultrapowers of finitary algebras, and one might expect this to have contradictory consequences.As a possible step towards proving his conjecture, Bankston [2] showed that no elementary SP-class of finitary algebras can be dually equivalent to CompHaus. However, it was subsequently proved in [1] that the same holds for any SP-class of finitary algebras, using an argument independent of ultrapowers.

publication date

  • December 1, 1984