LEADER 04852nam 22008415 450 001 9910299768903321 005 20220415191736.0 010 $a1-4471-6485-7 024 7 $a10.1007/978-1-4471-6485-2 035 $a(CKB)3710000000331859 035 $a(EBL)1967837 035 $a(OCoLC)899495713 035 $a(SSID)ssj0001424500 035 $a(PQKBManifestationID)11891908 035 $a(PQKBTitleCode)TC0001424500 035 $a(PQKBWorkID)11383628 035 $a(PQKB)10498149 035 $a(DE-He213)978-1-4471-6485-2 035 $a(MiAaPQ)EBC1967837 035 $a(PPN)183520432 035 $a(EXLCZ)993710000000331859 100 $a20150105d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aIndex analysis $eapproach theory at work /$fby R. Lowen 205 $a1st ed. 2015. 210 1$aLondon :$cSpringer London :$cImprint: Springer,$d2015. 215 $a1 online resource (477 p.) 225 1 $aSpringer Monographs in Mathematics,$x1439-7382 300 $aDescription based upon print version of record. 311 $a1-4471-6484-9 320 $aIncludes bibliographical references and index. 327 $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. 330 $aA featured review of the AMS describes the author?s earlier work in the field of approach spaces as, ?A landmark in the history of general topology?. In this book, the author has expanded this study further and taken it in a new and exciting direction.   The number of conceptually and technically different systems which characterize approach spaces is increased and moreover their uniform counterpart, uniform gauge spaces, is put into the picture. An extensive study of completions, both for approach spaces and for uniform gauge spaces, as well as compactifications for approach spaces is performed. A paradigm shift is created by the new concept of index analysis.   Making use of the rich intrinsic quantitative information present in approach structures, a technique is developed whereby indices are defined that measure the extent to which properties hold, and theorems become inequalities involving indices; therefore vastly extending the realm of applicability of many classical results. The theory is then illustrated in such varied fields as topology, functional analysis, probability theory, hyperspace theory and domain theory. Finally a comprehensive analysis is made concerning the categorical aspects of the theory and its links with other topological categories. Index Analysis will be useful for mathematicians working in category theory, topology, probability and statistics, functional analysis, and theoretical computer science. 410 0$aSpringer Monographs in Mathematics,$x1439-7382 606 $aGeometry 606 $aAlgebra 606 $aOrdered algebraic structures 606 $aApproximation theory 606 $aFunctional analysis 606 $aTopology 606 $aProbabilities 606 $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006 606 $aOrder, Lattices, Ordered Algebraic Structures$3https://scigraph.springernature.com/ontologies/product-market-codes/M11124 606 $aApproximations and Expansions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12023 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aTopology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28000 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aGeometry. 615 0$aAlgebra. 615 0$aOrdered algebraic structures. 615 0$aApproximation theory. 615 0$aFunctional analysis. 615 0$aTopology. 615 0$aProbabilities. 615 14$aGeometry. 615 24$aOrder, Lattices, Ordered Algebraic Structures. 615 24$aApproximations and Expansions. 615 24$aFunctional Analysis. 615 24$aTopology. 615 24$aProbability Theory and Stochastic Processes. 676 $a514.325 700 $aLowen$b R$4aut$4http://id.loc.gov/vocabulary/relators/aut$0534675 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299768903321 996 $aIndex analysis$91522422 997 $aUNINA