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Research Article | Open Access

Core compactness of ordered topological spaces

Yuxu Chen, Hui Kou( )
Department of Mathematics, Sichuan University, Chengdu 610064, China
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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?

Keywords

directed spacecore compactnessScott topologyclosed subsetsspectrum
CLC number: 54A10, 54A20, 06B35

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AIMS Mathematics
Volume 8 Issue 2,
February 2023
Pages 4862-4874
DOI: 10.3934/math.2023242

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Chen Y, Kou H. Core compactness of ordered topological spaces. AIMS Mathematics, 2023, 8(2): 4862-4874. https://doi.org/10.3934/math.2023242

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Received: 19 September 2022
Revised: 06 November 2022
Accepted: 24 November 2022
Published: 15 February 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)