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Cartesian Closed Subcategories of \(CONT_{\ll }^{{\kern 8pt}\ast }\)

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Abstract

Let CONT ≪ be the category of continuous domains and Scott continuous mappings that preserve the way-below relation on domains. Let ω-ALG ≪ be the full subcategory of CONT ≪ consisting of all countably based algebraic domains, and F I N be the category of finite posets and monotone mappings. The main result proved in this paper is that F I N is the largest Cartesian closed full subcategory of ω-ALG ≪. On the other hand, it is shown that the algebraic L-domains form a Cartesian closed full subcategory of ALG ≪.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Jiangsu Normal University, 221116, Xuzhou, China

    Xiaoyong Xi

  2. Department of Mathematics, Yangzhou University, 225002, Yangzhou, China

    Qingyu He

  3. College of Science, Hohai University, 210024, Nanjing, China

    Zhijun Lu

Authors
  1. Xiaoyong Xi
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  2. Qingyu He
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  3. Zhijun Lu
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Corresponding author

Correspondence to Xiaoyong Xi.

Additional information

Supported by the NSF of China (11361028,11401514, 61300153) and University Science Research Project of Jiangsu Province (15KJD110006)

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Xi, X., He, Q. & Lu, Z. Cartesian Closed Subcategories of \(CONT_{\ll }^{{\kern 8pt}\ast }\) . Order 33, 289–298 (2016). https://doi.org/10.1007/s11083-015-9366-8

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  • DOI: https://doi.org/10.1007/s11083-015-9366-8

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