形式背景的AE-仿紧性  

AE-paracompactness of formal contexts

作　　者：吴国俊 徐罗山[1] WU Guo-jun;XU Luo-shan(Department of Mathematics,Yangzhou University,Yangzhou 225002,China)

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《高校应用数学学报（A辑）》2022年第1期101-108,共8页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11671008);江苏省高校品牌专业建设工程(PPZY2015B109)。

摘　　要：利用拓扑学的思想定义了形式背景的AE-仿紧性,给出了AE-仿紧背景的充分条件,研究了AE-仿紧背景的若干性质.证明了AE-仿紧性被适当的信息态射所保持,对一类闭嵌入子背景是遗传的.在以形式背景为对象,信息态射为态射的范畴FCC中,给出了两个形式背景乘积对象的表示,证明了两个AE-仿紧背景的乘积对象还是AE-仿紧的.This paper defines AE-paracompactness of formal contexts by using the idea of topology. Some sufficient conditions for AE-paracompact contexts are given. It is proved that AEparacompactness is preserved by certain information morphisms and that AE-paracompactness is hereditary for certain closed embedded sub-contexts. The representation for the object of a product of two formal contexts is given in the category FCC with formal contexts as objects and information morphisms as morphisms. It is proved that the object of a product of two AE-paracompact contexts is still an AE-paracompact context.

关 键 词：形式背景 拓扑 AE-仿紧性 信息态射 范畴 

分 类 号：O153.1[理学—数学] O189.1[理学—基础数学]