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New representations of algebraic domains and algebraic L-domains via closure systems

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Abstract

Closure systems (spaces) play an important role in characterizing certain ordered structures. In this paper, FinSet-bounded algebraic closure spaces are introduced, and then used to provide a new approach to constructing algebraic domains. Then, a special family of algebraic closure spaces, algebraic L-closure spaces, are used to represent algebraic L-domains. Next, algebraic approximate mappings are defined and serve as the appropriate morphisms between algebraic closure spaces, respectively, algebraic L-closure spaces. On the categorical level, we show that algebraic closure spaces (respectively, algebraic L-closure spaces,) each equipped with algebraic approximate mappings as morphisms, are equivalent to algebraic domains (respectively, algebraic L-domains) with Scott continuous functions as morphisms.

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Notes

  1. In this paper, for any set X, we write \(F\sqsubseteq X\) to denote that F is a finite subset of X,

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 11771134). We would like to thank the anonymous reviews for their helpful comments and valuable suggestions. Moreover, we are very grateful to our editor Michael Mislove for his many help in the processing of this paper.

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Authors and Affiliations

  1. School of Mathematics, Hunan Institute of Science and Technology, Yueyang, 414006, Hunan, China

    Mingyuan Wu

  2. College of Mathematics and Statistics, Key Laboratory of High Performance Computing and Stochastic Information Processing, Hunan Normal University, Changsha, 410012, Hunan, China

    Lankun Guo

  3. School of Mathematics, Hunan University, Changsha, 410082, Hunan, China

    Qingguo Li

Authors
  1. Mingyuan Wu
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  2. Lankun Guo
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  3. Qingguo Li
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Correspondence to Qingguo Li.

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Communicated by Michael Mislove.

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Wu, M., Guo, L. & Li, Q. New representations of algebraic domains and algebraic L-domains via closure systems. Semigroup Forum 103, 700–712 (2021). https://doi.org/10.1007/s00233-021-10209-7

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