【摘要】 设E是一个A rch im edean R iesz空间,a∈E,Φ≠A E,则有如下的两个结论:1)由a生成的a-拓扑空间E是一个H ausdorff空间;2)若以下条件之一成立,则由A生成的A-拓扑空间E是一个H ausdorff空间:(a)子集{a:a∈A}有上界;(b)E具有强单位元;(c)若E=C(X),其中X是一个局部紧H ausdorff空间.更多还原

【Abstract】 Let E be an Archimedean Riesz space,a∈E,Φ≠AE.In this paper,two main results are obtained as follows: 1) The topological space E equipped with the a-topology is a Hausdorff space.2) If one of the following conditions holds,then the topological space E equipped with the A-topology is a Hausdorff space:(a) the subset {｜a｜∶a∈A} has an upper bound in E;(b) E has a strong unit;(c) in the case of E=C(X) where X is a locally compact Hausdorff space.更多还原