Lω-空间中的ω-Urysohn分离性

ω-Urysohn Separation in Lω-spaces

在Lω-空间中引入分子网和理想的ωθ*-极限点、ωθ*-聚点等概念,证明ω-Urysohn空间中分子网和理想的ωθ*-极限点均唯一等特征性质,并证明ω-Urysohn分离性是可ω-遗传的,在(ω1,ω2)-同胚和(ω1,ω2)θ-同胚映射下是拓扑不变的,在满层条件下是任意可乘的,而且是R.Lowen意义下好的推广等性质。

In this paper, the concepts of ω-Urysohn seperation axiom, ω-limit point （ω-cluster point） of molecular nets and ideals are defined. The .characterizations of ω-Urysohn seperation are systematically discussed. The propeties of ω-Urysohn seperation, such as, the ω-limit point of a molecular net and an ideal is only in ω-Urysohn spaces, are obtained. That ω-Urysohn seperation is hereditary, arbitrary multiplicative under condition of full-stratum, topological invariant under （ωl, ω2）-homeomorphic order- homorphism and （ωl, ω2）-homeomorphic order-homorphism, and the good extension in the sense of R. Lowen, are proved.