MV-Algebras as Sheaves of l-groups on Fuzzy Topological Spaces

TL;DR

This paper introduces fuzzy sheaves as a generalization of sheaves over fuzzy topological spaces and provides a representation theorem for a class of MV-algebras using MV-sheaves of lattice-ordered Abelian groups.

Contribution

It develops the concept of fuzzy sheaves and establishes a representation theorem linking MV-algebras with MV-sheaves of Abelian -groups on fuzzy topological spaces.

Findings

Fuzzy sheaves generalize classical sheaves to fuzzy topologies.

Representation of MV-algebras via MV-sheaves of -groups.

Connection between MV-topological spaces and MV-algebras.

Abstract

We introduce the concept of fuzzy sheaf as a natural generalisation of a sheaf over a topological space in the context of fuzzy topologies. Then we prove a representation for a class of MV-algebras in which the representing object is an MV-sheaf of lattice-ordered Abelian groups, namely, a fuzzy sheaf in which the base (fuzzy) topological space is an MV-topological space and the stalks are Abelian $\ell$-groups.