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L-拟序集上的广义Alexandroff拓扑
引用本文:张奇业,郑崇友.L-拟序集上的广义Alexandroff拓扑[J].模糊系统与数学,2002,16(1):13-17.
作者姓名:张奇业  郑崇友
作者单位:首都师范大学,数学系,北京,100037
基金项目:国家自然科学基金资助项目 (199710 5 9)
摘    要:在一类特殊的 L -拟序集上定义广义 Alexandroff拓扑 ,限制到通常的拟序集上就是 Alexandroff拓扑 ,并且该拓扑可以由其上的一族 Alexandroff拓扑取并得到。还证明任意一个拓扑空间的拓扑都可以表示为某个 L-拟序集上的广义 Alexandroff拓扑。

关 键 词:拓扑  拟序集  L-拟序集  L-单调映射  广义Alexandroff拓扑
文章编号:1001-7402(2002)01-0013-05
修稿时间:2001年4月20日

Generalized Alexandroff Topologies on L-Quasi Ordered Sets
ZHANG Qi-ye,ZHENG Chong-you.Generalized Alexandroff Topologies on L-Quasi Ordered Sets[J].Fuzzy Systems and Mathematics,2002,16(1):13-17.
Authors:ZHANG Qi-ye  ZHENG Chong-you
Abstract:In this paper,the generalized Alexandroff topology on an L-quasi ordered set is constructed, where L denotes a completely distributive lattice in which 1 is a molecule, it is exactly an Alexandroff topology when restricted to the ordinary quasi ordered set.It is proved that the generalized Alexandroff topology on an L-quasi ordered set (X,e) can be obtained by the join of a family of the Alexandroff topologies on X, and a topology on any topological space can be represented as a generalized Alexandroff topology on an L-quasi ordered set.
Keywords:Topology  Quasi Ordered Set  L-Quasi Ordered Set  L-Monotonic Mapping  Generalized Alexandroff Topology
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