Fuzzy points and attachment

In this paper a binary relation between L-sets, called attachment, is defined by means of a suitable family of completely coprime filters in L. Examples are given using several kinds of lattice-ordered algebras and a class of attachments is determined whose elements generalize Pu-Liu’s quasi-coincidence relation. Mapping any L-set on X to the set of the attached L-points one gets a frame map from the L-powerset L to the powerset P(SX) of the set SX of L-points on X. This allows one to define functors from the category L-Top of L-topological spaces either to the category Top of topological spaces or to the category TopSys of topological systems. A comparison with the hypergraph functor is also included.