Hyperclones Determined by Total-Parts of Hyper-relations

Abstract

This paper studies sets  of hyper-operations preserving relations on power set without emptyset. For a particular property of a relation, such a set  is hyperclone. We consider relations having total part exactly from Rosenberg's classes of relations.  By investigating nontrivial equivalence relations,  central relations and regular relations as total part, we show that sets of hyper-operations preserving such hyper-relations are maximal hyperclones.