Abstract: The category of additive generalized algebraic lattices with lower homomorphisms is equivalent to the category of T₀-topological spaces with continuous mappings ([11]). Follow the view, in this paper, using the generalized way below relation, the greatest system of subsets ([11]) and the lower homomorphisms ([12]) as tools, the notion of normal is defined, and Urysohn Lemma, Tietze extension theorem are constructed.

Key words: Complete lattice, Additive property, Generalized algebraic lattice, Lower homomorphism