{"product_id":"9780792373186","title":"Many Valued Topology and its Applications","description":"\u003ch1\u003eMany Valued Topology and its Applications\u003c\/h1\u003e \u003ch2\u003eHöhle, Ulrich\u003c\/h2\u003e \u003cp\u003eThe 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. \u003cem\u003eMany Valued  Topology and Its\u003c\/em\u003e \u003cem\u003eApplications\u003c\/em\u003e 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. \u003cbr\u003e  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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2001-04-30\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9780792373186\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4615-1617-0\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 382\u003c\/p\u003e ","brand":"Springer US","offers":[{"title":"Default Title","offer_id":46544941285516,"sku":"9780792373186","price":98.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780792373186.jpg?v=1775756703","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9780792373186","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}