The Measurement Topology and the Density Topology of Posets
Received:September 12, 2017  Revised:April 27, 2018
Key Word: essential topology   density topology   measurement topology   continuous poset   basis  
Fund ProjectL: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).
Author NameAffiliation
Xuxin MAO College of Science, Nanjing University of Aeronautics and Astronautics, Jiangsu 210016, P. R. China 
Luoshan XU Department of Mathematics, Yangzhou University, Jiangsu 225002, P. R. China 
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      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.
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