After some preliminaries, the set of generators of a generalized equal
ity relation (T-indistinguishability operator) is studied. This set is
identified with the set of the eigenvectors of the relation. The rela
tion between the fuzzy and ''metric'' topologies derived from these eq
ualities is stablished. The concept of basis is introduced and the con
struction of a procedure in order to calcualte explicity a basis of a
T-indistinguishability operator, for T archimedean, is proposed.