摘要
本文讨论了General树上序拓扑的性质,其中特别讨论了族正规性、仿紧性、可度量性等。其中给出宽度为有限的General树拓扑空间的度量化定理,这是Lutzer的线性序拓扑空间度量化定理的一个推广。根据Milner和王尚志最近的结果表明:线性序拓扑空间可度量化的充要条件是它可表示为某些同构于实数子集的集合的直和。可以得到一构造性结果:具有有限宽度的T_2—GTS可度量当且仅当它可以表示为某些实数子集的直和。
The paper discusses some properties of general tree space and investigatescollective normality, metrizablity and paracompactness of general tree spacewith finite width. The main results are follows: GTS with finite widthis collection normal if and only if it is T_2-space; T_2-GTS with finitewidth is metrizable if and only if it has G_δ-diagonal T_2-GTS with finitewidth is metrizable if and only if it is the sum of some subsets each one ofwhich is isomorphic some subsets of real number.
关键词
线性
序拓扑空间
General树
linear ordered topological space
general linear ordered toplogical space
general tree
