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

Luz Victoria De La Pava; Ciro Russo

doi:10.1007/s00500-020-04944-2

paper

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

arXiv:1909.10855 · doi:10.1007/s00500-020-04944-2

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 $ℓ$ -groups.

18 pages, to appear in Soft Computing doi: 10.1007/s00500-020-04944-2