Galois Connections*

Jean-Claude Falmagne () and Jean-Paul Doignon ()
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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

Chapter 8 in Learning Spaces, 2011, pp 133-150 from Springer

Abstract: 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.

Keywords: Binary Relation; Knowledge Structure; Closure Operator; Closure Space; Galois Connection (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-3-642-01039-2_8

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