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A Characterization Theorem for Continuous Lattices by Closure Spaces

  • Guozhi Ma
  • Lankun GuoEmail author
  • Cheng Yang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11511)

Abstract

The notion of closure spaces plays an important role in formal concept analysis, and there exists a close connection between formal concept analysis and lattice theory. In order to restructure continuous lattices, a special kind of complete lattices in Domain theory, this paper proposes a novel notion named relationally consistent F-augmented closure spaces. Then, the concept of F-approximable mappings between relationally consistent F-augmented closure spaces is introduced, which provides a representation of Scott continuous maps between continuous lattices. The final result is: the categories of relationally consistent F-augmented closure spaces and continuous lattices are equivalent.

Keywords

Closure space Approximable mapping Continuous lattice 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.College of Engineering and DesignHunan Normal University, ChangshaHunanPeople’s Republic of China
  2. 2.College of Mathematics and Statistics, Key Laboratory of High Performance, Computing and Stochastic Information ProcessingHunan Normal University, ChangshaHunanPeople’s Republic of China

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