广义Frame的谱空间(英文)

SPECTRUMS OF GENERALIZED FRAMES

本文在frame的范畴形式推广——广义frame上引进点、素元与谱空间的概念,并且证明任意广义frame都是完备、余完备的Cartesian闭范畴.进而说明一个广义frame上全体点与该广义frame上全体素元之间存在着范畴等价的关系,此关系不同于经典frame理论中相应的一一对应关系,并且讨论了广义Frame范畴与拓扑空间范畴之间的函子关系,最后,证明广义frame的谱空间是Sober空间。

In this paper, we introduce the concepts of points, prime elements and spec- trums in generalized frames which are generalizations of the corresponding concepts of frames in the sense of category, and show that any generalized frame is a complete, complete, Cartesian closed category. Moreover, we say that the category of all points of a generalized frame is equivalent to the the category of all prime elements of the generalized frame, and study the functor relation between the category of generalized frames and the category of topology spaces. Finally, we prove that the spectrums of generalized frames are sober.