Abstract
In this paper, we introduce the concepts of generalized continuous posets and present topological dualities for them. Moreover, we show that the category of generalized continuous posets and continuous morphisms is dually equivalent to the category of F-spaces and F-morphisms. In particular, some special cases are obtained, such as the topological representations for posets, domains, continuous lattices and join-semilattices.
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We would like to thank the anonymous reviewers for their professional comments and valuable suggestions.
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This work is supported by the National Natural Science Foundation of China (No.12231007).
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AS and QL wrote this paper. Both authors read and approved the final manuscript.
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Communicated by Jorge Picado.
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Shen, A., Li, Q. The Stone Representations for Generalized Continuous Posets. Appl Categor Struct 32, 3 (2024). https://doi.org/10.1007/s10485-023-09761-w
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DOI: https://doi.org/10.1007/s10485-023-09761-w