Galois Connections

Abstract

In vaxious preceding chapters, several one-to-one correspondences were established between particular collections of mathematical structures. For instance, Birkhoff’s Theorem 1.49 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. All these correspondences will be shown to 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, before the Sources section. We star the whole chapter because its content is more abstract, and not essential to the rest of this book.