Laterally closed lattice homomorphisms
A lattice homomorphism \(T: A\to B\) between two Archimedean vector lattices is called laterally closed if \(T(D)\) is a maximal orthogonal system in the band generated by \(T(A)\subset B\) for each maximal orthogonal system \(D\subset A\). The authors prove that any laterally closed \(T\) into a universally complete vector lattice \(B\) can be extended to a lattice homomorphism of the universal completion \(A^u\) into \(B\). This is an improvement of a result of \textit{M. Duhoux} and \textit{M. Meyer} [Ann. Soc. Sci. Bruxelles, Sér. I 98, 3--18 (1984; Zbl 0559.46003)].
scientific article; zbMATH DE number 5073015
scientific article