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, Volume 33, Issue 2, pp 289–298 | Cite as

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

  • Xiaoyong Xi
  • Qingyu He
  • Zhijun Lu
Article
  • 102 Downloads

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 .

Keywords

Cartesian closed category Algebraic domains Way-below relation Finite poset 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsJiangsu Normal UniversityXuzhouChina
  2. 2.Department of MathematicsYangzhou UniversityYangzhouChina
  3. 3.College of ScienceHohai UniversityNanjingChina

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