摘要
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 this paper we shall offer a separation axiom for frames inspired by the Hausdorff separation axiom for topological spaces. We call it separated condition. This is a condition on topology OX equivalent to the T O space X being Hausdorff. The class of separated frames includes that of strong Hausdorff frames and that of S frames. We shall show that the class of separated frames is a class closed under the formation of coproducts and subspaces, and the space Fil( L ) is Hausdorff for any separated frame L . Therefore there is a contravariant adjunction between the category TOP 2 of Hausdorff topological spaces and the category FRAM 2 of separated frames.