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?
Citation: Yuxu Chen, Hui Kou. Core compactness of ordered topological spaces[J]. AIMS Mathematics, 2023, 8(2): 4862-4874. doi: 10.3934/math.2023242
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?
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Yuxu Chen, Hui Kou. Core compactness of ordered topological spaces[J]. AIMS Mathematics, 2023, 8(2): 4862-4874. doi: 10.3934/math.2023242
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