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ZHANG Shanshan,LI Fei,YAO Wei.Axiomatic systems of Alexandrov spaces[J].Journal of Hebei University of Science and Technology,2017,38(4):352-359
Alexandrov空间的公理体系
Axiomatic systems of Alexandrov spaces
Received:December 12, 2016  Revised:March 08, 2017
DOI:10.7535/hbkd.2017yx04006
中文关键词:  拓扑学  Alexandrov空间  邻域系统  闭包算子  内部算子  导算子  特殊化序  完备生成格
英文关键词:topology  Alexandrov space  neighborhood system  closure operator  interior operator  derivation operator  specialization order  complete-generated lattice
基金项目:国家自然科学基金(11201112);中央高校基本科研业务专项资金项目(2017JC09);河北省高等学校科学技术研究项目重点项目(ZD2016047)
Author NameAffiliationE-mail
ZHANG Shanshan School of Science Hebei University of Science and Technology Shijiazhuang  
LI Fei School of Science Beijing Forest University feifei_1004@bjfu.edu.cn 
YAO Wei School of Science Hebei University of Science and Technology Shijiazhuang  
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中文摘要:
      为了研究Alexandrov空间的内部公理体系和序方面的特征,利用点集拓扑学和Locale理论中的已有结论,将各结构限制到Alexandrov空间的框架中,得到Alexandrov空间的等价刻画。研究结果表明Alexandrov空间在范畴意义下同构于Alexandrov邻域系统、Alexandrov闭包算子、Alexandrov内部算子、Alexandrov导算子等,T0的Alexandrov空间同构于偏序集、对偶等价于完全生成格。Alexandrov空间可以用邻域系统、闭包算子、内部算子、导算子,特殊化序和无点化序进行等价刻画。
英文摘要:
      In order to study internel axiomatic systems and ordered features of Alexandrov spaces, with the help of some existed results in topology and locale theory, by restricting the related structures into Alexandrov setting, some equivalent descriptions are obtained. The results show that Alexandrov spaces are categorically isomorphic to Alexandrov neighborhood systems, Alexandrov closure operators, Alexandrov interior operators and Alexandrov derived operators; T0 Alexandrov spaces are isomorphic to posets and dual to complete-generated lattices. Alexandrov spaces can be completely characterized by neighborhood systems, closure operators, interior operators, derived system, the specialization order and the point-free order.
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