@article{Chen2023, 
author = {Yuxu Chen and Hui Kou},
title = {Core compactness of ordered topological spaces},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {2},
pages = {4862-4874},
keywords = {spectrum, Scott topology, directed space, core compactness, closed subsets},
url = {https://www.sciopen.com/article/10.3934/math.2023242},
doi = {10.3934/math.2023242},
abstract = {In this paper, we investigate the property of core compactness of ordered topological spaces. Particularly, we give a series of characterizations of the core compactness for directed spaces. Several results obtained in this paper are closely related to a long-standing open problem in Open problems in Topology (J. van Mill, G. M. Reed Eds., North-Holland, 1990): Which distributive continuous lattice's spectrum is exactly a sober locally compact Scott space?}
}