{"product_id":"index-analysis-r-lowen-9781447172666","title":"Index Analysis: Approach Theory at Work","description":"\u003cp\u003eThe featured review of the AMS describes the author's earlier work in the field of approach spaces as, 'A landmark in the history of general topology'. In this book, the author has expanded this study further and taken it in a new and exciting direction.\u003c\/p\u003e\u003cp\u003eThe number of conceptually and technically different systems which characterize approach spaces is increased and moreover their uniform counterpart, uniform gauge spaces, is put into the picture. An extensive study of completions, both for approach spaces and for uniform gauge spaces, as well as compactifications for approach spaces is performed. A paradigm shift is created by the new concept of index analysis.\u003c\/p\u003e\u003cp\u003eMaking use of the rich intrinsic quantitative information present in approach structures, a technique is developed whereby indices are defined that measure the extent to which properties hold, and theorems become inequalities involving indices; therefore vastly extending the realm of applicability of many classical results. The theory is then illustrated in such varied fields as topology, functional analysis, probability theory, hyperspace theory and domain theory. Finally a comprehensive analysis is made concerning the categorical aspects of the theory and its links with other topological categories.\u003c\/p\u003e\u003cp\u003e\u003ci\u003eIndex Analysis\u003c\/i\u003e will be useful for mathematicians working in category theory, topology, probability and statistics, functional analysis, and theoretical computer science.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e R. Lowen\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1447172663\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781447172666\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 09\/24\/2016\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 466\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.50lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.99d","brand":"R. Lowen","offers":[{"title":"Paperback","offer_id":48518498222335,"sku":"9781447172666","price":54.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_ebee0f59-7ad5-464d-810b-08e8cc8cb74d.jpg?v=1778734662","url":"https:\/\/www.whiterainbookhouse.com\/products\/index-analysis-r-lowen-9781447172666","provider":"WR Book House","version":"1.0","type":"link"}