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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
Axiomatic systems of Alexandrov spaces
Received:December 12, 2016  Revised:March 08, 2017
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
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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      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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