| The Measurement Topology and the Density Topology of Posets |
| Received:September 12, 2017 Revised:April 27, 2018 |
| Key Words:
essential topology density topology measurement topology continuous poset basis
|
| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11671008; 11101212) and the University Science Research Project of Jiangsu Province (Grant No.15KJD110006). |
|
| Hits: 1365 |
| Download times: 1292 |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2018.04.002 |
| View Full Text View/Add Comment |
