Titlebook: Galois Connections and Applications; K. Denecke,M. Erné,S. L. Wismath Book 2004 Springer Science+Business Media Dordrecht 2004 Algebra.Ari

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Complexity of Terms and the Galois Connection Id-Mod,tice of the lattice of all varieties of the type. We also generalize to the k-normal case the results of Graczynska ([Gra]) and Melnik ([Mel]) describing normal varieties and the mapping taking any variety to the least normal variety containing it.

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Graham Cox,Philip Lowe,Michael Winter The main steps in the development are:.Besides sporadic occurrences of adjunctions and Galois connections in important mathematical theorems, we discuss diverse contributions to a systematical theory of adjunction and residuation, and we touch on various applications to topology, logic, universal algebra and formal concept analysis.

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Adjunctions and Galois Connections: Origins, History and Development, The main steps in the development are:.Besides sporadic occurrences of adjunctions and Galois connections in important mathematical theorems, we discuss diverse contributions to a systematical theory of adjunction and residuation, and we touch on various applications to topology, logic, universal algebra and formal concept analysis.

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Adjunctions and Galois Connections: Origins, History and Development,other algebraic, topological, order-theoretical, categorical and logical theories..We sketch the development of Galois connections, both in their covariant form (adjunctions) and in the contravariant form (polarities) through the last three centuries and illustrate their importance by many examples.

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The Polarity between Approximation and Distribution,ation properties of the underlying ordered sets, as known from the theory of continuous posets (domains)..Every closure operation . on a locale (frame) . with join-dense range . gives rise to a polarity (Galois connection) induced by the relation . = {(.) : . ≤ . ? . ≤ .}. Using that polarity, we sh