Representations of MV-algebras by Sheaves

In this paper, inspired by methods of Bigard, Keimel and Wolfenstein, we develop an approach to sheaf representations of MV-algebras which combines two techniques for the representation of MV-algebras devised by Dubuc and Poveda and by Filipoiu and Georgescu. Following Davey approach, we use a subdirect representation of MV-algebras that is based on local MV-algebras. This leads to a sheaf representation of an MV-algebra with local stalks and base space the spectrum of its prime ideals. Further we obtain: $(a)$ a representation of any MV-algebras as MV-algebra of all global sections of a sheaf of local MV-algebras on $SpecA$; $(b)$ a representation of MV-algebras with $MinA$ compact as MV-algebra of all global sections of a Hausdorff sheaf of MV-chains on $MinA$, that is a Stone space; $(c)$ an adjunction between the category of all MV-algebras and the category of {it MV-algebraic spaces} $(X,F)$ where $X$ is a compact topological space and $F$ is a sheaf of MV-algebras with stalk...