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偏序集上的测度拓扑与稠拓扑
引用本文:毛徐新,徐罗山.偏序集上的测度拓扑与稠拓扑[J].数学研究及应用,2018,38(4):341-350.
作者姓名:毛徐新  徐罗山
作者单位:南京航空航天大学理学院, 江苏 南京 210016,扬州大学数学科学学院, 江苏 扬州 225002
摘    要:

收稿时间:2017/9/12 0:00:00
修稿时间:2018/4/27 0:00:00

The Measurement Topology and the Density Topology of Posets
Xuxin MAO and Luoshan XU.The Measurement Topology and the Density Topology of Posets[J].Journal of Mathematical Research with Applications,2018,38(4):341-350.
Authors:Xuxin MAO and Luoshan XU
Abstract:In this paper,the concepts of the essential topology and the density topology of dcpos are generalized to the setting of general posets.Basic properties of the essential topology and relations with other intrinsic topologies are explored.Comparisons between the density topology and the measurement topology are made.Via the essential topology,the density topology and the measurement topology,we obtain properties and characterizations of bases of continuous posets.We also provide some new conditions for a continuous poset to be an algebraic poset.
Keywords:essential topology  density topology  measurement topology  continuous poset  basis
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