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,T_0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。
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.
出处
《河北科技大学学报》
CAS
2017年第4期352-359,共8页
Journal of Hebei University of Science and Technology
基金
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)
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
topology
Alexandrov space
neighborhood system
closure operator
interior operator
derivation operator
specialization order
complete-generated lattice
