## A characterization of cone preserving mappings of quasiordered sets.(English)Zbl 1095.08001

Summary: A cone of a quasiordered set $$(A,Q)$$ is any $$U_Q(a)=\{x\in A : \langle a,x\rangle \in Q\}$$. A mapping $$f: A\to B$$ is a cone preserving mapping of $$(A,Q)$$ into $$(B,Q')$$ if $$f(U_Q(a))=U_{Q'}(f(a))$$ for each $$a\in A$$. We characterize these mappings by using certain relational inclusions. The result can be applied for the construction of a quotient quasiorder hypergroup.

### MSC:

 08A02 Relational systems, laws of composition 08A30 Subalgebras, congruence relations 20N20 Hypergroups