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It is proved that the category $\mathbb{EM}$ of extended multisets is duallyequivalent to the category $\mathbb{CHMV}$ of compact Hausdorff MV-algebraswith continuous homomorphisms, which is in turn equivalent to the category ofcomplete and completely distributive MV-algebras with homomorphisms thatreflect principal maximal ideals. Urysohn-Strauss's Lemma, Gleason's Theorem,and projective objects are also investigated for topological MV-algebras.

Compact Hausdorff MV-algebras: Structure, Duality and Projectivity