RE-proximities as fixed points of an operator on pseudo proximities

We show that the RE-proximities of Császár (1986) can be obtained as images of some natural operator defined on pseudo proximities. Considering the one-to-one correspondence between closed graph relations on the ultrafilter space (the so-called “nasses” of Haddad (1970)) and pseudo proximities, this operator is indeed the correspondent of an idempotent operator defined on nasses and based upon the concepts of equivalence kernel and domain of a nasse.