格上点式一致结构的刻划与点式度量化定理  

Characterizations of Pointwise Uniformities and Pointwise Metrization Theorems on Lattices

作　　者：史福贵[1] 郑崇友[2] 

机构地区：[1]北京理工大学数学系,北京100081 [2]首都师范大学数学系,北京100037

出　　处：《数学学报（中文版）》2002年第6期1127-1136,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(19971059)

摘　　要：本文通过对格上远域映射,特别是△-映射和＊-映射的性质的研究,给出了格上点式一致结构的若干简明刻划,证明了几个重要的格上点式度量化定理,并提出了与格上点式度量理论相协调的若干分离性公理.Abstract In this paper, some brief characterizations of pointwise uniformities on lattices are presented by means of remote-neighborhood mappings. A few pointwise metrization theorems are proved. Some separation axioms which are consistent with pointwise metric theorem are given.

关 键 词：格 点式度量化定理 点式一致结构 T2公理 完全T2公理 Urysohn公理 

分 类 号：O189.11[理学—数学]