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000725078 019__ $$a903958038
000725078 020__ $$a9781447164852$$qelectronic book
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000725078 0247_ $$a10.1007/978-1-4471-6485-2$$2doi
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000725078 035__ $$aSP(OCoLC)899495713$$z(OCoLC)903958038
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000725078 049__ $$aISEA
000725078 050_4 $$aQA614.92
000725078 08204 $$a514/.74$$223
000725078 1001_ $$aLowen, R.$$q(Robert),$$eauthor.
000725078 24510 $$aIndex analysis$$h[electronic resource] :$$bapproach theory at work /$$cR. Lowen.
000725078 264_1 $$aLondon :$$bSpringer,$$c2015.
000725078 300__ $$a1 online resource (xxi, 466 pages) :$$billustrations.
000725078 336__ $$atext$$btxt$$2rdacontent
000725078 337__ $$acomputer$$bc$$2rdamedia
000725078 338__ $$aonline resource$$bcr$$2rdacarrier
000725078 4901_ $$aSpringer Monographs in Mathematics,$$x1439-7382
000725078 504__ $$aIncludes bibliographical references and index.
000725078 5050_ $$aApproach spaces -- Topological and metric approach spaces -- Approach invariants -- Index analysis -- Uniform gauge spaces -- Extensions of spaces and morphisms -- Approach theory meets Topology -- Approach theory meets Functional analysis -- Approach theory meets Probability -- Approach theory meets Hyperspaces -- Approach theory meets DCPO?s and Domains -- Categorical considerations.
000725078 506__ $$aAccess limited to authorized users.
000725078 520__ $$aA 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. The 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. Making 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. Index Analysis will be useful for mathematicians working in category theory, topology, probability and statistics, functional analysis, and theoretical computer science.
000725078 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed January 29, 2015).
000725078 650_0 $$aIndex theory (Mathematics)
000725078 650_0 $$aTopological spaces.
000725078 77608 $$iPrint version:$$z9781447164845
000725078 830_0 $$aSpringer monographs in mathematics.
000725078 852__ $$bebk
000725078 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-1-4471-6485-2$$zOnline Access$$91397441.1
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000725078 980__ $$aEBOOK
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