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Galois Connections

In: Learning Spaces

Author

Listed:
  • Jean-Claude Falmagne

    (University of California, Irvine, Department of Cognitive Sciences, Institute of Mathematical Behavioral Sciences)

  • Jean-Paul Doignon

    (Université Libre de Bruxelles, Département de Mathématique)

Abstract

In various preceding chapters, a number of one-to-one correspondences were established between particular collections of mathematical structures. For instance, Birkhoff’s Theorem 3.8.3 asserts the existence of a one-to-one correspondence between the collection of all quasi ordinal spaces on a domain Q and the collection of all quasi orders on Q. We will show here that all these correspondences derive from natural constructions. Each derivation will be obtained from the application of a general result about ‘Galois connections.’ A compendium of the notation for the various collections and the three ‘Galois connections’ of main interest to us is given at the end of the chapter in Table 8.3 on page 148. We star the whole chapter because its content is more abstract than, and not essential to, the rest of this book.

Suggested Citation

  • Jean-Claude Falmagne & Jean-Paul Doignon, 2011. "Galois Connections," Springer Books, in: Learning Spaces, chapter 8, pages 133-150, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-01039-2_8
    DOI: 10.1007/978-3-642-01039-2_8
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