Categorical properties of compact Hausdorff MV-algebras. (English) Zbl 1430.06009
Author’s 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.
Reviewer: Anna Romanowska (Warsaw)
MSC:
| 06D35 | MV-algebras |
| 06E15 | Stone spaces (Boolean spaces) and related structures |
| 18B35 | Preorders, orders, domains and lattices (viewed as categories) |
Keywords:
compact MV-algebras; E-multiset; complete distributivity; extremal disconnectedness; projective MV-algebraReferences:
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