Lower homomorphisms on additive generalized algebraic lattices

Abstract

In this paper, with the additivity property ([8]), the generalized way-below relation ([15]) and the maximal system of subsets ([6]) as tools, we prove that all lower homomorphisms between two additive generalized algebraic lattices form an additive generalized algebraic lattice, which yields the classical theorem: the function space between T0-topological spaces is also a T0-topological space with respect to the pointwise convergence topology.