Locale范畴中的零维性  

Zero dimensionality in the Category of Locales

作　　者：贺伟[1] 罗懋康 

机构地区：[1]陕西师范大学数学系 [2]四川联合大学数学系

出　　处：《数学学报（中文版）》1998年第3期539-544,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金;国家教委博士点基金

摘　　要：本文讨论ｌｏｃａｌｅ的零维性质，主要结果有：（１）给出ｌｏｃａｌｅＡ的核映射（ｎｕｃｌｅｕｓ）构成的ｌｏｃａｌｅＮ（Ａ）中上确界的点式刻划，并得到了Ｎ（Ａ）的紧性与Ａ的紧性之间的关系；（２）给出零维ｌｏｃａｌｅ与ｃｏｈｅｒｅｎｔｌｏｃａｌｅ之间的关系，以及零维ｌｏｃａｌｅ的紧零维反射；（３）给出零维ｌｏｃａｌｅ范畴在ｌｏｃａｌｅ范畴中的刻划．In this paper, we investigate the zero dimensional property for locales, the main results are following: (1) The pointwise characterization of joins of nuclei in a locale is given, the relationship between compactness of a locale A and compactness of N(A) is obtained.(2) The compact zero dimensional refletion of a zero dimensional localeis obtained in much simple form. (3) The category theory characterization of the category of zero dimensional locales is obtained.

关 键 词：LOCALE范畴 零维locale 零维性 范畴 

分 类 号：O154[理学—数学]