By dealing with absolute retracts of l-groups we use a definition analogous to that applied by Halmos for the case of Boolean algebras. The main results of the present paper concern absolute convex retracts in the class of all archimedean l-groups and in the class of all complete l-groups.
Extensions of order bounded linear operators on an Archimedean vector lattice to its relatively uniform completion are considered and are applied to show that the multiplication in an Archimedean lattice ordered algebra can be extended, in a unique way, to its relatively uniform completion. This is applied to show, among other things, that any order bounded algebra homomorphism on a complex Archimedean almost -algebra is a lattice homomorphism.
We denote by the class of all abelian lattice ordered groups such that each disjoint subset of is finite. In this paper we prove that if , then the cut completion of coincides with the Dedekind completion of .
In the present paper we show that free -algebras can be constructed by applying free abelian lattice ordered groups.
A generalization of I. Dobrakov’s integral to complete bornological locally convex spaces is given.