论文部分内容阅读
在Ｆｒａｍｅ理论中，与拓扑空间中的Ｈａｕｓｄｏｒｆ分离公理相对应的分离公理已被较深入地研究，但其结果并不很理想．本文给出相对应于Ｈａｕｓｄｏｒｆ分离公理的另一种定义，称之为分离公理．并证明如把此分离公理应用于Ｓｐａ－ｔｉａｌｆｒａｍｅｓ－拓扑－之上，它将与Ｈａｕｓｄｏｒｆ分离公理完全等价，而且此分离公理对于Ｓｕｂｆｒａｍｅｓ以及Ｆｒａｍｅ的和运算有遗传性．同时进一步证明：由满足此分离公理的ｆｒａｍｅｓ组成的范畴ＦＲＡＭＥ与Ｈａｕｓｄｏｒｆ拓扑空间范畴ＴＯＰ是反变伴随的．
In Frame theory, the separation axiom corresponding to the Hausdorf separation axiom in topological space has been studied more deeply, but the result is not very satisfactory. In this paper, another definition corresponding to the Hausdorf seperation axiom is given, which is called the axiom of separation. And prove that if this separation axiom is applied to Spa-tialframes-topology, it will be completely equivalent to Hausdorf’s separation axioms, and this separation axiom is hereditary for summation of Subframes and Frames. At the same time, it is further proved that the category FRAME composed of the frames satisfying the separation axioms and the Hausdorf topological space category TOP are anti-variant concomitants.