Lower homomorphisms on additive generalized algebraic lattices
Keywords:Additivity, Generalized way below relation, Lower homomorphism, Upper adjoint
In this paper, with the additivity property, the generalized way-below relation and the maximal system of subsets 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.
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