可加广义代数格上的Tietze扩张定理

Tietze Extension Theorem on Additive Generalized Algebraic Lattice

可加的广义代数格范畴与T0拓扑空间范畴相等价,从这个观点出发,作者把可加广义代数格作为一个闭集格,在其上建立Urysohn引理和Tietze扩张定理．这是拓扑理论在格上的一种新推广,有助于格上拓扑理论的研究和广义连续格理论的应用．

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.