偏序集上的测度拓扑与稠拓扑

The Measurement Topology and the Density Topology of Posets

英文关键词:essential topology  density topology  measurement topology  continuous poset  basis

中文摘要:

      

英文摘要:

      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.