Core compactness of ordered topological spaces

Core compactness of ordered topological spaces

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 i...

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Veröffentlicht in:AIMS mathematics 2023, Vol.8 (2), p.4862-4874
Hauptverfasser: Chen, Yuxu, Kou, Hui
Format: Artikel
Sprache:eng
Schlagworte:
closed subsets
core compactness
directed space
scott topology
spectrum
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Zusammenfassung: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?
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2023242