Title: Compact Hausdorff MV-algebras: Structure, Duality and Projectivity,
Abstract: It is proved that the category $\mathbb{EM}$ of extended multisets is dually
equivalent to the category $\mathbb{CHMV}$ 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.