Abstract
It is proved that the category of extended multisets is dually equivalent to the category of compact Hausdorff MV-algebras with continuous homomorphisms, which is in turn equivalent to the category of complete and completely distributive MV-algebras with homomorphisms that reflect principal maximal ideals. Urysohn–Strauss’s Lemma, Gleason’s Theorem, and projective objects are also investigated for topological MV-algebras. Among other things, it is proved that the only MV-algebras in which Urysohn–Strauss’s Lemma holds are Boolean algebras and that the projective objects in the category of compact Hausdorff MV-algebras are precisely the ones having the 2-element Boolean algebras as factor.
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