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OverviewThe 20th Century brought the rise of General Topology. It arose from the effort to establish a solid base for Analysis and it is intimately related to the success of set theory. Many Valued Topology and Its Applications seeks to extend the field by taking the monadic axioms of general topology seriously and continuing the theory of topological spaces as topological space objects within an almost completely ordered monad in a given base category C. The richness of this theory is shown by the fundamental fact that the category of topological space objects in a complete and cocomplete (epi, extremal mono)-category C is topological over C in the sense of J. Adamek, H. Herrlich, and G.E. Strecker. Moreover, a careful, categorical study of the most important topological notions and concepts is given - e.g., density, closedness of extremal subobjects, Hausdorff's separation axiom, regularity, and compactness. An interpretation of these structures, not only by the ordinary filter monad, but also by many valued filter monads, underlines the richness of the explained theory and gives rise to new concrete concepts of topological spaces - so-called many valued topological spaces. Hence, many valued topological spaces play a significant role in various fields of mathematics - e.g., in the theory of locales, convergence spaces, stochastic processes, and smooth Borel probability measures. In its first part, the book develops the necessary categorical basis for general topology. In the second part, the previously given categorical concepts are applied to monadic settings determined by many valued filter monads. The third part comprises various applications of many valued topologies to probability theory and statistics as well as to non-classical model theory. These applications illustrate the significance of many valued topology for further research work in these important fields. Full Product DetailsAuthor: Ulrich HöhlePublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: Softcover reprint of the original 1st ed. 2001 Dimensions: Width: 15.50cm , Height: 2.00cm , Length: 23.50cm Weight: 0.605kg ISBN: 9781461356431ISBN 10: 1461356431 Pages: 382 Publication Date: 24 October 2012 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsI Categorical Foundations.- 1 Categorical Preliminaries.- 2 Partially Ordered Monads.- 3 Categorical Basis of Topology.- II Many Valued Topology.- 4 Quantic Basis of Filter Theory.- 5 Many Valued Topological Spaces.- 6 Many Valued Convergence Theory.- III Applications of Many Valued Topology.- 7 Stochastic Metrics.- 8 Stochastic Processes.- 9 Probability Measures.- 10 Topologies on M-Valued Sets.- A.1 Regularity based on ortholattices.- A.2 Topologization of Menger spaces.- Author Index.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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