On Hyper Co-Clones

In this paper, we study closed sets of relations that are preserved by hyperoperations. We examine three already known Galois connections between hyperoperations and relations, and show that none of them induces a relational clone. We also introduce the notion of extended co-clone, and prove that there is a Galois connection (rPol, rInv) between extended hyperoperations on A and relations on non-void subsets of A with the property that rInv F is an extended co-clone. Moreover, we show that the three previously known classes of hyperclones can be defined by rPol.