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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
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