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Connections

  • Austin Melton
  • Bernd S. W. Schröder
  • George E. Strecker
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 598)

Abstract

It is well-known that Galois connections are useful in describing some situations that occur naturally in computer science and mathematics; and recently it has been shown that Lagois connections, which are closely related to Galois connections, are similarly useful. Thus, it is natural to ask if there are not common generalizations of Galois and Lagois connections which would be useful in both disciplines. In this paper we investigate several such generalizations. The primary one, called “connections”, was defined and first investigated in 1982 by H. Crapo. We present a hierarchy of connections from (general) connections to Lagois and Galois connections, and we establish properties of them. We also give examples in both computer science and mathematics.

key words

connection Galois connection Lagois connection semi-inverse poset system closure operator interior operator retraction operator 

AMS subject classification

Primary: 06A15, 06A10 Secondary: 68F05, 68F99, 54B99 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Austin Melton
    • 1
  • Bernd S. W. Schröder
    • 2
  • George E. Strecker
    • 2
  1. 1.Department of Computing and Information SciencesKansas State UniversityManhattanUSA
  2. 2.Department of MathematicsKansas State UniversityManhattanUSA

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