Syntactic homomorphisms (Q1093743)

Let two groupoids (E,.), (F,*) be given together with a one-to-one mapping \(\phi\) : \(E\to F\). Then a mapping h is called a syntactical homomorphism if \(h(x)=\phi (x)\) for all \(x\in E\) and \(h(y.z)=h(y)*h(z)\). A theorem concerning syntactical homomorphisms is proved and an application to topological linear spaces is shown.