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Monoidal Topology describes an active research area that, after various past proposals on how to axiomatize 'spaces' in terms of convergence, began to emerge at the beginning of the millennium. It combines Barr's relational presentation of topological spaces in terms of ultrafilter convergence with Lawvere's interpretation of metric spaces as small categories enriched over the extended real half-line. Hence, equipped with a quantale V (replacing the reals) and a monad T (replacing the ultrafilter monad) laxly extended from set maps to V-valued relations, the book develops a categorical theory of (T,V)-algebras that is inspired simultaneously by its metric and topological roots. The book highlights in particular the distinguished role of equationally defined structures within the given lax-algebraic context and presents numerous new results ranging from topology and approach theory to domain theory. All the necessary pre-requisites in order and category theory are presented in the book.
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Ordered algebraic structures --- 512 --- Algebra --- Topological semigroups. --- Representations of semigroups. --- 512 Algebra --- Topological semigroups --- Semigroupes topologiques --- Représentations de groupes
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Ordered algebraic structures --- 512 --- Algebra --- 512 Algebra --- Compact groups --- Groupes compacts --- Groupes compacts. --- Topological semigroups --- Semigroupes topologiques --- Topological semigroups. --- Fonctions presque-periodiques
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The analytical and topological theory of semigroups : trends and developments : [based on a conference held Jan. 30 - Feb. 4, 1989, hosted by the Mathematisches Forschungsinstitut Oberwolfach]
Topological semigroups --- Topological groups --- Groups, Topological --- Continuous groups --- Semigroups --- Semigroupes topologiques
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Topological semigroups. --- Semigroupes topologiques --- Analyse harmonique abstraite --- Algebres de lie --- Analyse harmonique abstraite --- Algebres de lie
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Topological semigroups. --- Semigroupes topologiques --- Algebres topologiques --- C star algebres --- Algebres topologiques --- C star algebres
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