Abstract
A subcategory of the category CONT of continuous dcpos is called topologically cartesian closed(tcc for short) if it is closed with respect to finite topological products and function spaces equipped with the Isbell topology. We prove that a full subcategory of CONT is tcc if and only if it is cartesian closed (by means of category) and the Isbell topology of function spaces coincides with the Scott topology (this is why we use the notion“tcc”).The main result of this paper is that the category of FS domains (resp., F-FS domains) is the largest tcc full subcategory of the category of pointed continuous dcpo’s (resp., continuous dcpo’s), where a continuous dcpo P is a F-FS domain iff P is a finite amalgam of FS domains.
This work is supported by the NSF of China, the SFEM of China and the Project of “Excellent Scholars Crossing Centuries” of the Education Ministry of China.
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Kou, H., Luo, M. (2001). The Largest Topologically Cartesian Closed Categories of Domains as Topological Spaces. In: Keimel, K., Zhang, GQ., Liu, YM., Chen, YX. (eds) Domains and Processes. Semantic Structures in Computation, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0654-5_4
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DOI: https://doi.org/10.1007/978-94-010-0654-5_4
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