| 格上点式一致结构的刻划与点式度量化定理 |
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| 引用本文： | 史福贵,郑崇友. 格上点式一致结构的刻划与点式度量化定理[J]. 数学学报, 2002, 45(6): 1127-113. DOI: cnki:ISSN:0583-1431.0.2002-06-011 |
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| 作者姓名： | 史福贵 郑崇友 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金资助项目（19971059） |
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| 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.
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| 关 键 词： | 点式一致结构 点式度量 T_2 公理 完全T_2 公理Urysohn公理 |
| 文章编号： | 0583-1431(2002)06-1127-10 |
| 修稿时间： | 2001-06-18 |
Characterizations of Pointwise Uniformities and Pointwise Metrization Theorems on Lattices |
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| Fu Gui SHI. Characterizations of Pointwise Uniformities and Pointwise Metrization Theorems on Lattices[J]. Acta Mathematica Sinica, 2002, 45(6): 1127-113. DOI: cnki:ISSN:0583-1431.0.2002-06-011 |
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| Authors: | Fu Gui SHI |
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| Affiliation: | Fu Gui SHI (Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P. R. China)Chong You ZHENG (Department of Mathematics, Capital Normal University, Beijing 100037, P. R. China) |
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| Abstract: | 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. |
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| Keywords: | Pointwise uniformity Pointwise metric T_2 axiom Complete T_2 axiom Urysohn axiom |
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