1993
DOI: 10.1111/j.1749-6632.1993.tb52513.x
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Abstract: The rudiments of the theoly of Galois connections (or residuation theory, as it is sometimes called) are provided, together with many examples and applications. Galois connections occur in profusion and are well known to most mathematicians who deal with order theory; they seem to be less known to topologists. However, because of their ubiquity and simplicity, they (like equivalence relations) can be used as an effective research tool throughout mathematics and related areas. If one recognizes that a Galois co… Show more

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Cited by 141 publications
(74 citation statements)
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“…When L = 2, these are precisely the classical uniformities, described in terms of axialities [5] (cf. also [6,Section 5]).…”
Section: Definition 43 We Say That a Pair (X D) Consisting Of A Sementioning
confidence: 99%
See 2 more Smart Citations
“…When L = 2, these are precisely the classical uniformities, described in terms of axialities [5] (cf. also [6,Section 5]).…”
Section: Definition 43 We Say That a Pair (X D) Consisting Of A Sementioning
confidence: 99%
“…Nowadays many authors prefer to work with Galois connections in the covariant form by its convenience (the survey [5] contains a list of references to this form). We refer to this dualized form as a residuated pair: a residuated pair between the partially ordered sets A and B is a pair (f, g) of order-preserving maps f : A → B and g : B → A such that…”
Section: Residuated L-valued Uniform Spacesmentioning
confidence: 99%
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“…A more detailed survey of Galois adjoints can be found in Erné et al (1993) and for Galois adjoints in a more physical perspective we refer to . A pair of maps f * :…”
Section: Sasaki Adjunctionmentioning
confidence: 99%
“…The result of the approximation can also be formalized using a poset P A , ≤ A . Then, the approximation relation between those two posets can be defined as a Galois surjection [20,21,2,7,6] :…”
Section: Representation Systemsmentioning
confidence: 99%